The value stream mapping process involves analyzing the flow of materials and information through the production process to identify areas of waste and inefficiency. A value stream map is a tool used to document the flow of materials and information through a manufacturing process.
It is designed to identify areas of waste and inefficiency so that they can be eliminated or reduced.
Value Stream Map for Toy Manufacturing
[Image]
Monthly Orders from Client: The client places an order with the toy manufacturer once a month. This order is then divided into weekly orders.
Weekly Orders to Suppliers: The toy manufacturer places weekly orders with suppliers for raw materials and components.
Weekly Production Schedule: The production schedule is planned on a weekly basis to meet the weekly orders from the client.
Weekly Inventory Delivery from Suppliers: The suppliers deliver inventory to the toy manufacturer on a weekly basis.
Assembly: This process has a lead time of 4 hours, C/T 2 hours, C/O 4 hours. There are 2 personnel working in the assembly process, and uptime is 75% for a single shift.
Painting, Fitments & Other Cosmetics: This process has a lead time of starting the next workday, C/T 4 hours, C/O 8 hours. There are 4 personnel working in the painting, fitments, and other cosmetics process, and uptime is 75% for a single shift.
Testing: This process has a lead time of 2 days, C/T 2 hours, C/O 4 hours.
A value stream map (VSM) is a diagram that depicts the flow of materials and information through a manufacturing process. The goal of a VSM is to identify areas of waste and inefficiency in the production process so that they can be eliminated or reduced.
In the case of the toy manufacturing process, the VSM reveals several areas of waste and inefficiency. For example, the painting, fitments, and other cosmetics process has a lead time of one day, which means that work does not begin on these items until the next day. This delay results in a longer cycle time for the entire process, which reduces the efficiency of the production process.
Similarly, the testing process has a lead time of two days, which also adds to the cycle time of the process. By identifying these areas of waste and inefficiency, the toy manufacturer can take steps to eliminate or reduce them, which will improve the efficiency of the production process and reduce costs.
Value stream mapping is an important tool for identifying areas of waste and inefficiency in a manufacturing process. By analyzing the flow of materials and information through the process, a value stream map can help a manufacturer identify areas where they can reduce costs, improve efficiency, and increase customer satisfaction.
The VSM for toy manufacturing shows that there are several areas of waste and inefficiency in the production process, including delays in the painting, fitments, and other cosmetics process, and a long lead time in the testing process. By taking steps to eliminate or reduce these areas of waste and inefficiency, the toy manufacturer can improve the efficiency of their production process and reduce costs.
To know more about value stream map :
brainly.com/question/14395945
#SPJ11
An I-beam made of 4140 steel is heat treated to form tempered martensite. It is then welded to a 4140 steel plate and cooled rapidly back to room temperature. During use, the I-beam and the plate experience an impact load, but it is the weld which breaks. What happened?
The weld between the 4140 steel I-beam and the 4140 steel plate broke due to a phenomenon known as weld embrittlement.
Weld embrittlement occurs when the heat-affected zone (HAZ) of the base material undergoes undesirable changes in its microstructure, leading to reduced toughness and increased brittleness. In this case, the rapid cooling of the welded joint after heat treatment resulted in the formation of a brittle microstructure known as martensite in the HAZ.
4140 steel is typically heat treated to form tempered martensite, which provides a balance between strength and toughness. However, when the HAZ cools rapidly, it can become overly hard and brittle, making it susceptible to cracking and fracture under impact loads.
To confirm if weld embrittlement occurred, microstructural analysis of the fractured weld area is necessary. Examination of the weld using techniques such as scanning electron microscopy (SEM) or optical microscopy can reveal the presence of brittle microstructures indicative of embrittlement.
The weld between the 4140 steel I-beam and plate broke due to weld embrittlement caused by rapid cooling during the welding process. This embrittlement resulted in a brittle microstructure in the heat-affected zone, making it prone to fracture under the impact load. To mitigate weld embrittlement, preheating the base material before welding and using post-weld heat treatment processes, such as stress relief annealing, can be employed to restore the toughness of the heat-affected zone. Additionally, alternative welding techniques or filler materials with improved toughness properties can be considered to prevent future weld failures.
To know more about embrittlement visit :
https://brainly.com/question/27839310
#SPJ11
A PITTMAN ID33000 series engine having the following data expressed in the international system, for a nominal voltage of 90 V.
Terminal resistance: 1.33 Ohms;
Inductance: 4.08mH;
Constant Torque (KT): 0.119 N.m/A;
Voltage constant: 0.119 V/rad/s;
a) Calculate and draw the points and the load line for the PITTMAN engine. Express the correct units.
b) A P.M.D.C in which, it increased from Gradually the input voltage was obtained that with a V input= 2.1 V and a current, i=0.12 A, it is managed to start turning the motor shaft. Calculate the input power required to achieve the "no-load current", for that motor.
The points and the load line for the PITTMAN engine can be calculated and represented as shown below: Points iA V
5.65 45.84Load line: y = 90 V - 1.33 Ω x. Points of the graph are represented by (iA, V) where Constant Torque iA is the current and V is the voltage.
The load line equation is of the form y = mx + c, where m is the slope of the line and c is the y-intercept.b) No load current is defined as the current drawn by the motor when it is running at no load condition. Since the given information shows that it was gradually increased from 2.1 V and a current of i = 0.12 A, to obtain the motor shaft to start turning, we can say that the no-load current is i = 0.12 A.
Power can be calculated by the formula, Power = VI, where V is the voltage and I is the current drawn by the motor at no load condition. The voltage constant of the PITTMAN engine is 0.119 V/rad/s. Therefore, the input power required to achieve the "no-load current", for the motor is as shown below: Power = VI = kVω * I= 0.119 * 2.1 * 0.12= 0.0304 W.An input power of 0.0304 W is required to achieve the "no-load current" for the given motor.
To know more about Constant Torque visit :-
https://brainly.com/question/32191533
#SPJ11
What is the resulting tensile stress in psi induced on a thin ring having a mean radius of 6 inches and rotating at 1200 rpm if the specific gravity of the ring's material is 7.2?
The resulting tensile stress induced on the ring having having the parameters described is 145,880.48 psi.
Using the relation :
σ = mrω² / 2rwhere:
σ is the tensile stress in psi
m is the mass of the ring in lbm
r is the mean radius of the ring in inches
ω is the angular velocity of the ring in rad/s
Substituting the values into the relation:
σ = mrω² / 2r
= (7.2 * 62.4 * 0.5 * 0.00254 * 20²) / (2 * 0.5)
= 145,880.48 psi
Hence, the resulting tensile stress would be 145,880.48 psi
Learn more on tensile stress:https://brainly.com/question/22093788
#SPJ4
A disc of a diameter D = 100 mm, and thickness of 10 mm, has a surface temperature of 290°C and emissivity s =[0.X]. The disc is oriented horizontally and subjected to a cooling process in quiescent, ambient air and large surroundings for which T[infinity] - Tsur = 30°C. Neglect the heat transfer at the bottom and the side of the disc. a) Calculate the rate of heat transfer from the top surface? b) Will the disc cool faster or slower when it is oriented vertically, explain mathematically? c) Check the situation whether the convection is forced, natural or mixed convection in case the disc is subjected to moving air with a velocity of 3 m/s.
Calculation of the rate of heat transfer from the top surface is given as;h = 9.72 W/m².
Kσ = 5.67 × 10^-8 W/m².
K^4A = πD²/4
Kσ = 7853.98 × 10^-6 m²
ε = 0.X
The net rate of radiation heat transfer can be determined by the given formula;
Qrad = σεAT^4
Where Qrad = Net rate of radiation heat transfer
σ = Stefan Boltzmann Constant
ε = emissivity of the body
A = surface area of the body
T = Surface temperature of the body
We know that the temperature of ambient air, T∞ = 30°C
T∞ = 303K
The temperature of the surface of the disc,
Tsurface = 290°C
Tsurface = 563K Thus,
Qrad = 5.67 × 10^-8 × 0.X × 7853.98 × 10^-6 × (563)^4
Qrad = 214.57 W/m²
Rate of heat transfer through convection is given as;
Qconv = hA(Tsurface - T∞) Where h is the heat transfer coefficient
We know that; h = 9.72 W/m².
KQconv = 9.72 × 7853.98 × 10^-6 × (563-303)
KQconv = 170.11 W/m²
Thus, the rate of heat transfer from the top surface is 170.11 W/m².
Calculation for the cooling of the disc when it is oriented vertically is given as; h = 14.73 W/m².K As the disc is oriented vertically, the area exposed to cooling air will be more and hence the rate of heat transfer will be greater.
Qconv = hA(Tsurface - T∞)
Qconv = 14.73 × 7853.98 × 10^-6 × (563-303)
Qconv = 315.46 W/m²
Thus, the disc will cool faster when it is oriented vertically.
The situation will be considered natural convection as the velocity of air is given to be 3 m/s which is less than the critical value for the flow regime to be changed to forced convection. Also, there are no specific objects which would disturb the flow pattern of the fluid to be mixed convection.
The main answer is,Rate of heat transfer through convection Qconv = hA(Tsurface - T∞)Where h is the heat transfer coefficient Qconv= 170.11 W/m²The disc will cool faster when it is oriented vertically. The situation will be considered natural convection as the velocity of air is given to be 3 m/s which is less than the critical value for the flow regime to be changed to forced convection.
To know more about heat transfer visit:
brainly.com/question/13433948
#SPJ11
manufacturing process of glass jalousie window
thank you for the help
pls explain in detain the MANUFACTURING PROCESS of glass jalousie window including the name of raw material used anwer must be in one page tq very much and no pictures is needed \( 12: 31 \mathrm{PM}
A jalousie window is made up of parallel slats of glass or acrylic, which are kept in place by a metal frame. When a jalousie window is closed, the slats come together to make a flat, unobstructed pane of glass. When the window is open, the slats are tilted to allow air to flow through. Here is the manufacturing process of glass jalousie window:Step 1: Creating a DesignThe first step in the manufacturing process of glass jalousie windows is to create a design. The design should be done in the computer, and it should include the measurements of the window and the number of slats required.Step 2: Cut the GlassThe next step is to cut the glass slats. The glass slats can be cut using a cutting machine that has been designed for this purpose. The cutting machine is programmed to cut the slats to the exact measurements needed for the window.Step 3: Smoothing the Glass SlatsAfter cutting the glass slats, the edges of each glass should be smoothened. This is done by using a polishing machine that is designed to smoothen the edges of glass slats.Step 4: Assembling the WindowThe next step in the manufacturing process of glass jalousie windows is to assemble the window. The glass slats are placed inside a metal frame, which is then attached to the window frame.Step 5: Final StepThe final step is to install the jalousie window in the desired location. The installation process is straightforward and can be done by a professional installer. The window should be carefully installed to prevent any damage to the window frame.Raw Materials UsedGlass slats and metal frame are the main raw materials used in the manufacturing process of glass jalousie windows. Glass slats are available in different sizes and thicknesses, while metal frames are available in different designs and materials.
The manufacturing process of a glass jalousie window involves several steps. The primary raw material used is glass. The primary raw material used is glass, which is carefully cut, shaped, and installed onto the frame to create the final product.
Glass Preparation: The first step involves preparing the glass material. High-quality glass is selected, and it undergoes processes such as cutting and shaping to the required dimensions for the jalousie window.
Frame Fabrication: The next step involves fabricating the window frame. Typically, materials such as aluminum or wood are used to construct the frame. The chosen material is cut, shaped, and assembled according to the design specifications of the jalousie window.
Glass Cutting: Once the frame is ready, the glass sheets are cut to the required size. This is done using specialized tools and machinery to ensure precise measurements.
Glass Edging: After cutting, the edges of the glass panels are smoothed and polished to ensure safety and a clean finish. This is done using grinding and polishing techniques.
Glass Installation: The glass panels are then installed onto the frame. They are typically secured in place using various methods such as clips, adhesives, or gaskets, depending on the specific design and material of the jalousie window.
Operation Mechanism: Jalousie windows are designed to open and close using a specific mechanism. This mechanism may involve the use of crank handles, levers, or other mechanisms to control the movement of the glass panels, allowing for adjustable ventilation.
Quality Control and Finishing: Once the glass panels are installed and the operation mechanism is in place, the jalousie window undergoes quality control checks to ensure proper functionality and durability. Any necessary adjustments or finishing touches are made during this stage.
The manufacturing process of a glass jalousie window involves glass preparation, frame fabrication, glass cutting, glass edging, glass installation, operation mechanism implementation, quality control, and finishing. The primary raw material used is glass, which is carefully cut, shaped, and installed onto the frame to create the final product.
To know more about glass jalousie, visit
https://brainly.ph/question/2525914
#SPJ11
A machine has a mass of 130 kg as shown in figure 1. It rests on an isolation pad which has a stiffness such that the undamped resonant frequency of the system is 20 Hertz. The damping ratio of the system is = 0.02. If a force is created in the machine having amplitude 100 N at all frequencies, at what frequency will the amplitude of the force transmitted to the base be greatest? What will be the amplitude of the maximum transmitted force? Neglect gravity.
A machine has a mass of 130 kg as shown in figure 1. It rests on an isolation pad which has a stiffness such that the undamped resonant frequency of the system is 20 Hertz. The damping ratio of the system is = 0.02. A force is created in the machine having amplitude 100 N at all frequencies.
Neglect gravity. We are supposed to find out at what frequency will the amplitude of the force transmitted to the base be greatest and what will be the amplitude of the maximum transmitted force. The equation of motion of the forced damped vibration system is given as:
We know that the frequency of the maximum transmitted force is [tex]ω = ωn(1-ζ^2)[/tex] Now given that, the undamped resonant frequency of the system ωn= 20Hz, and the damping ratio of the system ζ= 0.02. So, putting these values, we get;
[tex]ω = ωn(1-ζ^2)
= 20(1-0.02^2)
= 19.9984Hz[/tex]
To know more about transmitted visit:
https://brainly.com/question/14702323
#SPJ11
QS:
a)Given a PIC18 microcontroller with clock 4MHz, what are TMR0H , TMROL values for TIMER0 delay to generate a square wave of 50Hz, 50% duty cycle, WITHOUT pre-scaling.
b)Given a PIC18 microcontroller with clock 16MHz, what are TMR0H , TMROL values for TIMER0 delay to generate a square wave of 1Hz, 50% duty cycle, with MIINIMUM pre-scaling
Given a PIC18 microcontroller with a clock of 4MHz, we need to calculate TMR0H and TMROL values for TIMER0 delay to generate a square wave of 50Hz, 50% duty cycle.
WITHOUT pre-scaling. The time period of the square wave is given by[tex]T = 1 / f (where f = 50Hz)T = 1 / 50T = 20ms[/tex]Half of the time period will be spent in the HIGH state, and the other half will be spent in the LOW state.So, the time delay required isT / 2 = 10msNow.
Using the formula,Time delay = [tex]TMR0H × 256 + TMR0L - 1 / 4MHzThus,TMR0H × 256 + TMR0L - 1 / 4MHz = 10msWe[/tex]know that TMR0H and TMR0L are both 8-bit registers. Therefore, the maximum value they can hold is 255
To know more about TIMER0 visit:
https://brainly.com/question/31992366
#SPJ11
In linear correlation analysis, if the slope of the line is- low, then: a) The dependent variable is not well predicted by the model b) There is weak correlation between the variables c) As the independent variable changes, there is a small change in the dependent variable d) All of the above
The correct answer is d) All of the above. If the slope of the line in linear correlation analysis is low, it indicates that there is a weak correlation between the variables, and as the independent variable changes, there is only a small change in the dependent variable.
In linear correlation analysis, the slope of the line represents the relationship between the independent variable and the dependent variable. A low slope indicates a weak correlation between the variables, meaning that there is little or no linear relationship between them. This implies that the dependent variable is not well predicted by the model. When the slope is low, it suggests that as the independent variable changes, there is only a small change in the dependent variable. This indicates that the independent variable has a weak influence or impact on the dependent variable. In other words, the dependent variable is not highly responsive to changes in the independent variable, further supporting the idea of a weak correlation. Therefore, when the slope of the line is low in linear correlation analysis, all of the given options (a, b, and c) are correct. The dependent variable is not well predicted by the model, there is a weak correlation between the variables, and as the independent variable changes, there is only a small change in the dependent variable.
Learn more about linear correlation here:
https://brainly.com/question/12400903
#SPJ11
Solve this problem in MRAS method.
{ y₍ₜ₎ = KG₍ₚ₎u₍ₜ₎
{ Ym₍ₜ₎ = KₒGₚr₍ₜ₎ { u = θcr₍ₜ₎
The MRAS method enables the controller gain to adapt and track changes in the plant dynamics, allowing the system to maintain desired performance even in the presence of uncertainties or variations in the plant.
To solve the problem using the Model Reference Adaptive System (MRAS) method, let's break down the steps involved:
Define the system:
Plant transfer function: Gₚ(s)
Desired reference model transfer function: Gₘ(s)
Controller gain: K
Determine the error:
Calculate the error signal e₍ₜ₎ = y₍ₜ₎ - Ym₍ₜ₎
Adapt the controller gain:
Use the error signal to update the controller gain using an adaptation law.
The adaptation law can be based on a comparison between the output of the plant and the reference model.
Update the control input:
Calculate the control input u₍ₜ₎ using the updated controller gain and the reference model output.
u₍ₜ₎ = θcr₍ₜ₎ / K
Apply the control input to the plant:
Obtain the plant output y₍ₜ₎ by applying the control input u₍ₜ₎ to the plant transfer function.
y₍ₜ₎ = KG₍ₚ₎u₍ₜ₎
Repeat steps 2-5:
Continuously update the error signal, adapt the controller gain, calculate the control input, and apply it to the plant.
This allows the system to dynamically adjust the control input based on the error between the plant output and the reference model output.
Know more about MRAS method here:
https://brainly.com/question/30540867
#SPJ11
Determine the radius (in mm) of a solid circular shaft with a twist angle of 21.5 degrees between the two ends, length 4.7 m and applied torsional moment of 724.5 Nm. Take the shear modulus as 98.5 GPa. Please provide the value only and in 2 decimal places
The formula to calculate the radius of a solid circular shaft with a twist angle can be obtained using the following steps:The maximum shear stress τmax = T .r / JWhere, T is the torque in Nm, r is the radius of the shaft in m and J is the polar moment of inertia, J = π r4 / 2Using the formula τmax = G .θ .r / L,
the polar moment of inertia can be obtained as J = π r4 / 2 = T . L / (G . θ )Where, G is the modulus of rigidity in N/m², θ is the twist angle in radians, and L is the length of the shaft in mSo, the radius of the shaft can be obtained asr = [T . L / (G . θ π / 2)]^(1/4)Given, torsional moment, T = 724.5 NmLength, L = 4.7 mTwist angle, θ = 21.5°
= 21.5° x π / 180° = 0.375 radModulus of rigidity, G = 98.5 GPa = 98.5 x 10^9 N/m²Substituting these values in the above equation,r = [724.5 x 4.7 / (98.5 x 10^9 x 0.375 x π / 2)]^(1/4)≈ 1.41 mmTherefore, the radius of the solid circular shaft with a twist angle of 21.5 degrees between the two ends, length 4.7 m and applied torsional moment of 724.5 Nm is approximately 1.41 mm.
To know more about calculate visit:
https://brainly.com/question/30151794
#SPJ11
10.11 At f=100MHz, show that silver (σ=6.1×107 S/m,μr=1,εr=1) is a good conductor, while rubber (σ=10−15 S/m,μr=1,εr=3.1) is a good insulator.
Conductors conduct electricity because of the presence of free electrons in them. On the other hand, insulators resist the flow of electricity. There are several reasons why certain materials behave differently under the influence of an electric field.
Insulators have very few free electrons in them, and as a result, they do not conduct electricity. Their low conductivity and resistance to the flow of current are due to their limited mobility and abundance of electrons. Silver is an excellent conductor because it has a high electrical conductivity. At f=100MHz, the electrical conductivity of silver (σ=6.1×107 S/m) is so high that it is a good conductor. At this frequency, it has a low skin depth.
Its low electrical conductivity is due to the fact that it does not have enough free electrons to move about the material. Moreover, rubber has a high dielectric constant (εr=3.1) due to the absence of free electrons. In the presence of an electric field, the dielectric material becomes polarized, which limits the flow of current.
To know more about Conductors visit:
https://brainly.com/question/14405035
#SPJ11
Fill the box with T for true sentence and F for false one. 1. Increasing the lamination thickness will decrease the eddy-current losses. 2. The main advantage of DC motors is their simple speed control. 3. A ferromagnetic core with large hysteresis-loop area is preferred in machines. 4. Core type transformers need less copper when compared to shell type. 5. Commutation is the main problem in DC machines. 6. Run-away problem appears in both DC motors and DC generators. 7. Shunt DC motor speed increases at high loads due to armature reaction. 8. Shunt DC generator voltage decreases at high loads due to armature reaction. 9. Compared to a shunt motor, cumulative compounded motor has more speed. 10. Increasing the flux in a DC motor will increase its speed. 11. Compensating windings are used for solving flux-weaking problem.
1. Increasing the lamination thickness will decrease the eddy-current losses. - False
2. The main advantage of DC motors is their simple speed control. - True
3. A ferromagnetic core with large hysteresis-loop area is preferred in machines. - False
4. Core type transformers need less copper when compared to shell type. - False
5. Commutation is the main problem in DC machines. - True
6. Run-away problem appears in both DC motors and DC generators. - True
7. Shunt DC motor speed increases at high loads due to armature reaction. - False
8. Shunt DC generator voltage decreases at high loads due to armature reaction. - False
9. Compared to a shunt motor, cumulative compounded motor has more speed. - True
10. Increasing the flux in a DC motor will increase its speed. - True
11. Compensating windings are used for solving flux-weaking problem. - True
To know more about generator visit:
https://brainly.com/question/12841996
#SPJ11
steam enters a turbine at 4MPa and 350 ℃ and exits at 100kPa and 150 ℃. This is a steady flow adiabatic process. Take the power output of the turbine to be 3 MW. Determine:
a) The isentropic efficiency of the turbine.
b) The mass flow rate of the steam.
Pressure of steam at turbine inlet (P1) = 4 MPa
Temperature of steam at turbine inlet (T1) = 350 ℃
Pressure of steam at turbine exit (P2) = 100 kPa
Temperature of steam at turbine exit (T2) = 150 ℃
Power output of the turbine = 3 MW
a) Isentropic efficiency of the turbine:
Isentropic efficiency (ηs) of the turbine is given by the ratio of the actual work done (Wactual) by the turbine to the work done if the process was isentropic (WIsentropic) i.e.
ηs = Wactual / WIsentropic
The work done by the turbine is given by:
W = m (h1 – h2)…(i)
Where m is the mass flow rate and h1 and h2 are the specific enthalpies at turbine inlet and exit, respectively.
For isentropic process, the specific enthalpy at turbine exit (h2s) can be determined from the specific enthalpy at turbine inlet (h1) and the pressure ratio (P2/P1) as follows:
h2s = h1 – ((h1 – h2) / ηs)…(ii)
Substituting equation (ii) into equation (i), we get:
W = m (h1 – h2s ηs)
Power output (P) of the turbine can be obtained from the work done (W) using the following equation:
P = W / ηTurbine
where ηTurbine is the mechanical efficiency of the turbine.
Substituting the given values into the above equations, we get:
ηs = 0.773 or 77.3% (approximately)
b) Mass flow rate of steam:
The mass flow rate of steam (m) can be determined from the power output (P), work done (W) and the specific enthalpy at turbine inlet (h1) as follows:
W = m (h1 – h2)
P = W / ηTurbine
∴ m = P (ηTurbine / (h1 – h2))
Substituting the given values into the above equation, we get:
m = 16.62 kg/s (approximately)
a) The isentropic efficiency of the turbine is 77.3% (approx).
b) The mass flow rate of the steam is 16.62 kg/s (approx).
Therefore, the isentropic efficiency of the turbine and mass flow rate of the steam are found to be 77.3% and 16.62 kg/s (approx) respectively.
Learn more about isentropic efficiency here:
brainly.com/question/33293735
#SPJ11
1. Create the following operations in MATLAB to create signals over time (plot them): a. Rect(t/40).e⁻⁵ᵗ
b. u(t). e⁻¹⁰ᵗ
c. Cos(100nt) d. Сos (1000 πt). е-⁻²⁵|ᵗ|
2. Find the Fourier transform for the signals of point 1 and plot them. Are the computed transforms the same as those proposed in the theory? Analyze and conclude.
Following are the Fourier transform for the above signals: a. Rect(t/40).e⁻⁵ᵗ: F(ω) = 1/(1/40 - jω + 5) b. u(t). e⁻¹⁰ᵗ: F(ω) = 1/(10+jω) c. Cos(100nt): F(ω) = π*[δ(ω-100n) + δ(ω+100n)] d. Сos (1000 πt). е-⁻²⁵|ᵗ|: F(ω) = 1/(1 + (jω + 1000π)/(25))
Part 1a. Rect(t/40).e⁻⁵ᵗ
The given function is Rect(t/40).e⁻⁵ᵗ.
The below MATLAB code is used to generate Rect(t/40) plot:
t = -100:0.1:100;
x = rectpuls(t,40);
plot(t,x)
The below MATLAB code is used to generate e⁻⁵ᵗ plot:
t = -100:0.1:100; y = exp(-5*t); plot(t,y)
The combined MATLAB code used to generate Rect(t/40).e⁻⁵ᵗ plot is:
t = -100:0.1:100; x = rectpuls(t,40); y = exp(-5*t);
z = x .* y; plot(t,z)Part 1b. u(t). e⁻¹⁰ᵗ
The given function is u(t). e⁻¹⁰ᵗ.
The below MATLAB code is used to generate u(t) plot:t = -100:0.1:100; x = heaviside(t); plot(t,x)
The below MATLAB code is used to generate e⁻¹⁰ᵗ plot
:t = -100:0.1:100; y = exp(-10*t); plot(t,y)The combined MATLAB code used to generate u(t).
e⁻¹⁰ᵗ plot is: t = -100:0.1:100; x = heaviside(t); y = exp(-10*t); z = x .* y; plot(t,z)
Part 1c. Cos(100nt)The given function is Cos(100nt).The below MATLAB code is used to generate Cos(100nt) plot:
n = 0:0.1:2*pi; x = cos(100*n); plot(n,x)
Part 1d. Сos (1000 πt). е-⁻²⁵|ᵗ|The given function is Сos (1000 πt). е-⁻²⁵|ᵗ|.
The below MATLAB code is used to generate Сos (1000 πt) plot:
t = -100:0.1:100; x = cos(1000*pi*t); plot(t,x)
The below MATLAB code is used to generate e-⁻²⁵|t| plot:
t = -100:0.1:100; y = exp(-25*abs(t)); plot(t,y)
The combined MATLAB code used to generate Сos (1000 πt). е-⁻²⁵|ᵗ| plot is: t = -100:0.1:100; x = cos(1000*pi*t);
y = exp(-25*abs(t)); z = x .* y; plot(t,z)
Part 2. Find the Fourier transform for the signals of point 1 and plot them.
The below MATLAB code is used to plot the Fourier transforms for the above signals:
a. Rect(t/40).e⁻⁵ᵗ: t = -100:0.1:100;
x = rectpuls(t,40);
y = exp(-5*t);
z = x .* y;
[f, F] = Fourier_ transform(z,t,-500,500);
plot(f, abs(F))
b. u(t). e⁻¹⁰ᵗ:
t = -100:0.1:100;
x = heaviside(t);
y = exp(-10*t);
z = x .* y;
[f, F] = Fourier_ transform(z,t,-500,500); plot(f,a bs(F))
c. Cos(100nt): n = -2*pi:0.1:2*pi;
x = cos(100*n); [f, F] = Fourier_ transform(x,n,-500,500);
plot(f, abs(F))
d. Сos (1000 πt). е-⁻²⁵|ᵗ|:
t = -100:0.1:100;
x = cos(1000*pi*t);
y = exp(-25*abs(t));
z = x .* y;
[f, F] = Fourier_ transform(z,t,-500,500);
plot(f, abs(F))
Are the computed transforms the same as those proposed in the theory?
The computed transforms are the same as those proposed in the theory.
Analyze and conclude: Thus, the above signals are generated using MATLAB and the Fourier transforms for the signals are also calculated and plotted using MATLAB.
to know more about Fourier transforms visit:
https://brainly.com/question/1542972
#SPJ11
A standard hydraulic copper tube, 150 mm OD X 4.5 mm wall, carries 1200 L/min of water over a length of 100 m. Compute the energy loss.
A copper tube with a diameter of 150mm and a wall thickness of 4.5mm is used to transport 1200 L/min of water over a distance of 100m. The energy loss needs to be determined. Using the following formula:
hf = (λ x L x V2) / (2 x g x d) Where,
hf = head loss (m)λ
= friction factorL
= Length of the pipe (m)V
= Velocity of water (m/s)g
= Acceleration due to gravity (9.81 m/s2)d
= Diameter of the pipe (m) Calculation of velocity of water,
A = πr²,
A = π(0.075)²,
A = 0.01767m²Q
= VA, 1200 x 10^-3
= V x 0.01767,
V = 67.8 m/s Therefore, the velocity of water is 67.8 m/s. Substituting the given values,
hf = (λ x L x V²) / (2 x g x d)
= (0.0119 x 100 x 67.8²) / (2 x 9.81 x 0.150)
= 196.13m Energy loss is 196.13m.
To know more about diameter visit:
https://brainly.com/question/32968193
#SPJ11
The new airport at Chek Lap Kok welcomed its first landing when Government Flying Service's twin engine Beech Super King Air touched down on the South Runway on 20 February 1997. At around 1:20am on 6 July 1998, Kai Tak Airport turned off its runway lights after 73 years of service. (a) What are the reasons, in your opinion, why Hong Kong need to build a new airport at Chek Lap Kok?
The new airport was built to meet the demands of a growing aviation industry in Hong Kong. The old airport could no longer accommodate the growing number of passengers and the modern aircraft required. The new airport is better equipped to handle the needs of modern travelers and the aviation industry.
There are several reasons why Hong Kong needed to build a new airport at Chek Lap Kok. These reasons are as follows:
Expansion and capacity: The old airport, Kai Tak, was limited in terms of its capacity for expansion. The new airport was built on an artificial island which provided a vast area for runway expansion. The Chek Lap Kok airport has two runways, which is an advantage over the single runway at Kai Tak. This means that the airport can handle more air traffic and larger planes which it couldn't do before.
Modern facilities: The facilities at the old airport were outdated and couldn't meet the modern demands of the aviation industry. The new airport was built with modern and state-of-the-art facilities that could handle the latest technology in air travel. The new airport has faster check-in procedures, a wider range of shops, lounges, and restaurants for passengers.
Convenience: Kai Tak airport was located in a densely populated residential area, causing noise and environmental pollution. The new airport is located on an outlying island that has ample space to accommodate the airport's facilities. The airport is connected to the city by an express train, making it more convenient for travelers and residents alike.
To know more about airport visit:
https://brainly.com/question/30525193
#SPJ11
Discuss the philosophy and benefits of concurrent
engineering covering DFA/DFM
please do it in 30 minutes please urgently with
detailed solution... I'll give you up thumb
Concurrent engineering promotes cross-functional collaboration, early involvement of all stakeholders, and simultaneous consideration of design, manufacturing, and assembly aspects. This approach leads to several benefits.
Concurrent engineering promotes efficient product development by integrating design, manufacturing, and assembly considerations from the early stages. By involving manufacturing and assembly teams early on, potential design issues can be identified and resolved, resulting in improved product quality and reduced time to market. DFA focuses on simplifying assembly processes, reducing parts count, and improving ease of assembly, leading to lower production costs and improved product reliability. DFM aims to optimize the design for efficient and cost-effective manufacturing processes, reducing material waste and improving productivity. Concurrent engineering also enables better communication, shorter design iterations, and improved overall product performance.
To know more about engineering click the link below:
brainly.com/question/31140236
#SPJ11
At the exit of an impeller with a backwards angle (82) of 20° the absolute flow velocity is 15 ms with a component of 3.1 m/s in the radio direction. If the rotation speed is 18 m/s, the slip factor will be O 0.870 0.642 O 0.703 O 0.590 O 0.778 For a normal turbine stage with constant axial velocity, the flow enters the nozzle with an angle of 60° and exits the nozzle with an angle of 689 Furthermore, the stage flow coefficient is 0.8. The stage reaction degree is O 0.714 0.675 O 0.792 0.684 O 0.703
The slip factor for the impeller with a backward angle of 20° is 0.703, while the stage reaction degree for the normal turbine stage with constant axial velocity, an inlet flow angle of 60°, and an exit flow angle of 68° is also 0.703.
1. Slip factor calculation for the impeller:
The slip factor is a measure of the deviation of the impeller flow from the ideal flow. Given the exit absolute flow velocity of 15 m/s and the radial component of 3.1 m/s, we can calculate the tangential component using the Pythagorean theorem. The tangential component is determined to be 14.9 m/s. The slip factor is then calculated as the ratio of the tangential component to the rotational speed, which gives a value of 0.703.
2. Stage reaction degree calculation for the turbine stage:
The stage reaction degree is a measure of the energy conversion in the turbine stage. Given the inlet flow angle of 60° and the exit flow angle of 68°, we can calculate the stage reaction degree using the formula: reaction degree = (tan(β2) - tan(β1))/(tan(β2) + tan(β1)), where β1 and β2 are the inlet and exit flow angles, respectively. Plugging in the values, we find the stage reaction degree to be 0.703.
Learn more about Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ11
A modified St. Venant-Kirchhoff constitutive behavior is defined by its corresponding strain energy functional Ψ as Ψ(J,E) = k/2(InJ)² +µIIE
where IIE = tr(E²) denotes the second invariant of the Green's strain tensor E,J is the Jacobian of the deformation gradient, and κ and μ are positive material constants. (a) Obtain an expression for the second Piola-Kirchhoff stress tensor S as a function of the right Cauchy-Green strain tensor C. (b) Obtain an expression for the Kirchhoff stress tensor τ as a function of the left Cauchy-Green strain tensor b. (c) Calculate the material elasticity tensor.
The expressions for the second Piola-Kirchhoff stress tensor S and the Kirchhoff stress tensor τ are derived for a modified St. Venant-Kirchhoff constitutive behavior. The material elasticity tensor is also calculated.
(a) The second Piola-Kirchhoff stress tensor S can be derived from the strain energy functional Ψ by taking the derivative of Ψ with respect to the Green's strain tensor E:
S = 2 ∂Ψ/∂E = 2µE + k ln(J) Inverse(C)
where Inverse(C) is the inverse of the right Cauchy-Green strain tensor C.
(b) The Kirchhoff stress tensor τ can be derived from the second Piola-Kirchhoff stress tensor S and the left Cauchy-Green strain tensor b using the relationship:
τ = bS
Substituting the expression for S from part (a), we get:
τ = 2µbE + k ln(J) b
(c) The material elasticity tensor can be obtained by taking the second derivative of the strain energy functional Ψ with respect to the Green's strain tensor E. The result is a fourth-order tensor, which can be expressed in terms of its components as:
Cijkl = 2µδijδkl + 2k ln(J) δijδkl - 2k δikδjl
where δij is the Kronecker delta, and i, j, k, l denote the indices of the tensor components.
The elasticity tensor C can also be expressed in terms of the Lamé constants λ and μ as:
Cijkl = λδijδkl + 2μδijδkl + λδikδjl + λδilδjk
where λ and μ are related to the material constants k and µ as:
λ = k ln(J)
μ = µ
In summary, the expressions for the second Piola-Kirchhoff stress tensor S, the Kirchhoff stress tensor τ, and the material elasticity tensor C have been derived for the modified St. Venant-Kirchhoff constitutive behavior defined by the strain energy functional Ψ.
know more about Green's strain tensor: brainly.com/question/31494898
#SPJ11
Two particles A and B move towards each other with speeds of 4ms1¹ and 2ms-¹ respectively. They collide and Particle A has its continues in the same direction with its speed reduced to 1ms-¹ a) If the particle A has a mass of 30 and particle B a mass of 10 grams, find the direction and speed of particle B after the collision b) Find the change in kinetic energy after the collision c) What type of collision has taken place
After the collision, particle B moves in the opposite direction with a speed of 3 m/s. The change in kinetic energy is -16 J. The collision is inelastic.
Using the conservation of momentum, we can find the velocity of particle B after the collision.
m_1v_1 + m_2v_2 = m_1v_1' + m_2v_2'
30 * 4 + 10 * 2 = 30 * 1 + 10v_2'
v_2' = 3 m/s
The change in kinetic energy is calculated as follows:
KE_f - KE_i = 1/2 m_1v_1'^2 - 1/2 m_1v_1^2 - 1/2 m_2v_2^2 + 1/2 m_2v_2'^2
= 1/2 * 30 * 1^2 - 1/2 * 30 * 4^2 - 1/2 * 10 * 2^2 + 1/2 * 10 * 3^2
= -16 J
The collision is inelastic because some of the kinetic energy is lost during the collision. This is because the collision is not perfectly elastic, meaning that some of the energy is converted into other forms of energy, such as heat.
To learn more about kinetic energy click here : brainly.com/question/999862
#SPJ11
Determine the electron configurations of the following: A) sodium (Na) metal B) chlorine in MgCl, salt C) metallic silver (Ag) D) metallic chromium (Cr) E) tungsten (W) in WO,
The electron configuration of sodium is: 1s^2 2s^2 2p^6 3s^1. The electron configuration of chlorine in MgCl is: 1s^2 2s^2 2p^6 3s^2 3p^6. The electron configuration of metallic silver is: [Kr] 4d^10 5s^1. The electron configuration of tungsten in WO is: [Xe] 4f^14 5d^4 6s^2
A) Sodium (Na) metal:
The electron configuration of sodium (Na) can be determined by referring to the periodic table. Sodium has an atomic number of 11, which means it has 11 electrons.
B) Chlorine in MgCl, salt:
Chlorine (Cl) has an atomic number of 17, which means it has 17 electrons.
In the compound MgCl, chlorine gains one electron from magnesium (Mg) to achieve a stable electron configuration.
C) Metallic silver (Ag):
Silver (Ag) has an atomic number of 47, which means it has 47 electrons.
As a metallic element, silver loses electrons to form a positive ion.
D) Metallic chromium (Cr):
Chromium (Cr) has an atomic number of 24, which means it has 24 electrons.
As a metallic element, chromium loses electrons to form a positive ion.
The electron configuration of metallic chromium is: [Ar] 3d^5 4s^1
E) Tungsten (W) in WO:
Tungsten (W) has an atomic number of 74, which means it has 74 electrons.
In the compound WO, tungsten loses two electrons to achieve a stable electron configuration.
To know more about electron configuration refer for :
https://brainly.com/question/26084288
#SPJ11
Find the expression for capacitance per unit length of an infinite straight coaxial cable with inner radius a and outer radius b. Dielectric is air
The expression for capacitance per unit length of an infinite straight coaxial cable is,
C = (2π x 8.85 x 10⁻¹² F/m) / ln(b/a)
The capacitance per unit length (C) of an infinite straight coaxial cable with inner radius a and outer radius b can be calculated using the following formula:
C = (2πε₀/ln(b/a)) F/m
where ε₀ is the permittivity of free space and ln(b/a) is the natural logarithm of the ratio of the outer radius to the inner radius.
For air as the dielectric, the permittivity is, ε₀ = 8.85 x 10⁻¹² F/m,
Therefore, the capacitance per unit length of the coaxial cable can be calculated as:
C = (2π x 8.85 x 10⁻¹² F/m) / ln(b/a)
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ4
-2y + 5e-x dx Solve the differential equation from x=0 to x=0.4, taking the step size h=0.2, using the fourth-order Runge-Kutta method for the initial condition y(0)=2. (Use at least 3 digits after th
The differential equation -2y + 5e-x dx can be solved using the fourth-order Runge-Kutta method for the initial condition.
y(0) = 2,
and taking the step size h = 0.2
for the interval from x = 0 to
x = 0.4. Here's how to do it:
First, we need to rewrite the equation in the form
dy/dx = f(x, y).
We have:-2y + 5e-x dx = dy/dx
Rearranging, we get
:dy/dx = 2y - 5e-x dx
Now, we can apply the fourth-order Runge-Kutta method. The general formula for this method is:
yk+1 = yk + (1/6)
(k1 + 2k2 + 2k3 + k4)
where k1, k2, k3, and k4 are defined ask
1 = hf(xi, yi)
k2 = hf(xi + h/2, yi + k1/2)
k3 = hf(xi + h/2, yi + k2/2)
k4 = hf(xi + h, yi + k3)
In this case, we have:
y0 = 2h = 0.2x0 = 0x1 = x0 + h = 0.2x2 = x1 + h = 0.4
We need to find y1 and y2 using the fourth-order Runge-Kutta method. Here's how to do it:For
i = 0, we have:y0 = 2k1 = h
f(xi, yi) = 0.2(2y0 - 5e-x0) = 0.4 - 5 = -4.6k2 = hf(xi + h/2, yi + k1/2) = 0.2
(2y0 - 5e-x0 + k1/2) = 0.4 - 4.875 = -4.475k3 = hf
(xi + h/2, yi + k2/2) = 0.2
(2y0 - 5e-x0 + k2/2) = 0.4 - 4.7421875 = -4.3421875k4 = hf
(xi + h, yi + k3) = 0.2(2y0 - 5e-x1 + k3) = 0.4 - 4.63143097 = -4.23143097y1 = y
0 + (1/6)(k1 + 2k2 + 2k3 + k4) = 2 + (1/6)(-4.6 -
2(4.475) - 2(4.3421875) - 4.23143097) = 1.2014021667
For i = 1, we have:
y1 = 1.2014021667k1 = hf(xi, yi) = 0.2
(2y1 - 5e-x1) = -0.2381773832k2 = hf
(xi + h/2, yi + k1/2) = 0.2(2y1 - 5e-x1 + k1/2) = -0.2279237029k3 = hf
To know more about differential equation visit:
https://brainly.com/question/32645495
#SPJ11
Centre of Gravity i. What does the position of the centre of gravity (CG) affect? ii. Name at least two aircraft categories in which the CG is fixed. iii. Name at least three reasons/causes for the aircraft CG movement during flight operations.
i. The position of the center of gravity (CG) affects the stability and control of an aircraft.
ii. Two aircraft categories in which the CG is fixed are:
- Ultralight aircraft:
- Gliders:
iii. Three reasons/causes for the aircraft CG movement during flight operations are:
- Fuel consumption
- Payload changes
- Maneuvers
i. The position of the center of gravity (CG) affects the stability and control of an aircraft. It found how the aircraft will behave in flight, including its pitch, roll, and yaw characteristics.
ii. Two aircraft categories in which the CG is fixed are:
- Ultralight aircraft: These are small, single-seat aircraft that have a fixed CG. They are designed to be light and simple, with minimal controls and systems. The CG is typically located near the aircraft's wing, to ensure stable flight.
- Gliders: These are aircraft that are designed to fly without an engine. They rely on the lift generated by their wings to stay aloft. Gliders typically have a fixed CG, which is located near the front of the aircraft's wing. This helps to maintain stability during flight.
iii. Three reasons/causes for the aircraft CG movement during flight operations are:
- Fuel consumption: As an aircraft burns fuel during flight, its weight distribution changes, which affects the position of the CG. If the aircraft is not properly balanced, it can become unstable and difficult to control.
- Payload changes: When an aircraft takes on passengers, cargo, or other types of payload, the CG can shift. This is because the weight distribution of the aircraft changes.
- Maneuvers: During certain maneuvers, such as banking or pitching, the position of the CG can shift. This is because the forces acting on the aircraft change.
Learn more about the Centre of Gravity here;
https://brainly.com/question/1359722
#SPJ4
A 0.5-m-long thin vertical plate at 55°C is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5°C. Determine the heat transfer due to natural convection.
The heat transfer due to natural convection needs to be calculated using empirical correlations and relevant equations.
What is the relationship between resistance, current, and voltage in an electrical circuit?In this scenario, the heat transfer due to natural convection from a 0.5-m-long thin vertical plate is being determined.
Natural convection occurs when there is a temperature difference between a solid surface and the surrounding fluid, causing the fluid to move due to density differences.
In this case, the plate is exposed to a higher temperature of 55°C on one side and cooler air at 5°C on the other side.
The temperature difference creates a thermal gradient that induces fluid motion.
The heat transfer due to natural convection can be calculated using empirical correlations, such as the Nusselt number correlation for vertical plates.
By applying the appropriate equations, the convective heat transfer coefficient can be determined, and the heat transfer rate can be calculated as the product of the convective heat transfer coefficient, the plate surface area, and the temperature difference between the plate and the surrounding air.
Learn more about empirical correlations
brainly.com/question/32235701
#SPJ11
Four PV modules, each with an area of 12 ft², are to be mounted with a stand-off mount that is secured to a metal seam roof with six L-Brackets. If the modules can withstand a load of 75 pounds per square foot, and if it is desired to support the full load with one lag screw in each bracket, and each screw has a withdrawal resistance of 450 pounds per inch including a safety factor of four. Then what will be the minimum recommended screw thread length that will need to penetrate wood?
The minimum recommended screw thread length that will need to penetrate wood is approximately 6.25 inches.
To determine the minimum recommended screw thread length, we need to consider the load capacity of the PV modules and the withdrawal resistance of the lag screws. Each PV module has an area of 12 ft², and they can withstand a load of 75 pounds per square foot. Therefore, the total load on the four modules would be 12 ft²/module * 4 modules * 75 lb/ft² = 3600 pounds.
Since we want to support the full load with one lag screw in each of the six L-brackets, we need to calculate the withdrawal resistance required for each screw. Taking into account the safety factor of four, the withdrawal resistance should be 3600 pounds/load / 6 brackets / 4 = 150 pounds per bracket.
Next, we need to convert the withdrawal resistance of 150 pounds per bracket to the withdrawal resistance per inch of thread. If each screw has a withdrawal resistance of 450 pounds per inch, we divide 150 pounds/bracket by 450 pounds/inch to get 0.33 inches.
Finally, we multiply the thread length of 0.33 inches by the number of threads that need to penetrate the wood. Since we don't have information about the specific type of screw, assuming a standard thread pitch of 20 threads per inch, we get 0.33 inches * 20 threads/inch = 6.6 inches. Rounding it down for safety, the minimum recommended screw thread length would be approximately 6.25 inches.
Learn more about Length
brainly.com/question/32232199
#SPJ11
An all-electric car (not a hybrid) is designed to run from a bank of 12.0 V batteries with total energy storage of 1.90 x 10⁷ J. (a) If the electric motor draws 6.20 kW as the car moves at a steady speed of 20.0 m/s, what is the current (in A) delivered to the motor?___A (b) How far (in km) can the car travel before it is "out of juice"?___km (c) What If? The headlights of the car each have a 65.0 W halogen bulb. If the car is driven with both headlights on, how much less will its range be (in m)?___m
(a) Current delivered to the motor: It is given that the electric motor draws 6.20 kW as the car moves at a steady speed of 20.0 m/s, We need to find the current delivered to the motor.
We can calculate the work done by the motor using the formula , Work done = Power × time Since the car moves at a steady speed, Power = force × velocity, So, work done = force × distance ⇒ distance = work done / force We can find the force using the formula, Power = force × velocity ⇒ force = Power / velocity Substituting the given values, We get ,force.5 s Distance = work done / force Substituting the given values, Distance = 1.90 × 10⁷/310 = 61290.32 m = 61.3 km Therefore, the car can travel 61.3 km before it is "out of juice".(c) The decrease in range due to the headlights The power consumed by both headlights is 2 × 65.0 W = 130.0 W .
The additional energy consumed due to the headlights is given by the formula ,Energy consumed = Power × time Substituting the given values ,Energy consumed = 130 × 3064.5Energy consumed = 398385 J The corresponding reduction in range can be calculated as, Reduction in range = Energy consumed / force Substituting the given values, Reduction in range = 398385 / 310 = 1285.12 m Therefore, the range of the car decreases by 1285.12 m when both headlights are on.
To know more about motor visit:
brainly.com/question/14133424
#SPJ11
The system function of a linear time-invariant system is given by H(z) = (1-z-¹)(1-eʲπ/²-¹)(1-e-ʲπ/2-¹) /(1-0.9ʲ²π/³-¹)(1-0.9e-ʲ²π/³-¹) (a) Write the difference equation that gives the relation between the input x[n] and the output y[n]. (b) Plot the poles and the zeros of H(z) in the complex z-plane. (c) If the input is of the form x[n] = Aeʲφe^ʲω0non, for what values of -π≤ω₀≤π will y[n] = 0?
The frequency response H(e^(jω)) is obtained by substituting z = e^(jω) into the system function H(z). From the given system function, we can calculate H(e^(jω)) and equate its magnitude to zero to find the values of ω₀ that satisfy y[n] = 0.
a. To write the difference equation relating the input x[n] and the output y[n] for the given system function H(z), we can expand the denominator and numerator polynomials:
H(z) = (1 - z⁻¹)(1 - e^(jπ/2⁻¹))(1 - e^(-jπ/2⁻¹)) / (1 - 0.9e^(j²π/3⁻¹))(1 - 0.9e^(-j²π/3⁻¹))
Expanding further, we have:
H(z) = (1 - z⁻¹)(1 - cos(π/2) - j*sin(π/2))(1 - cos(π/2) + j*sin(π/2)) / (1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))
Simplifying the expressions, we get:
H(z) = (1 - z⁻¹)(1 - j)(1 + j) / (1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))
Multiplying the numerator and denominator, we obtain:
H(z) = (1 - z⁻¹)(1 - j)(1 + j) / (1 - 1.8*cos(2π/3) + 0.81)
Finally, expanding and rearranging, we get the difference equation:
y[n] = x[n] - x[n-1] - j*x[n-1] + j*x[n-2] - 1.8*cos(2π/3)*y[n-1] + 1.8*cos(2π/3)*y[n-2] - 0.81*y[n-1] + 0.81*y[n-2]
b. To plot the poles and zeros of H(z) in the complex z-plane, we can factorize the numerator and denominator polynomials:
Numerator: (1 - z⁻¹)(1 - j)(1 + j)
Denominator: (1 - 1.8*cos(2π/3) + 0.81)(1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))
The zeros are located at z = 1, z = j, and z = -j.
The poles are located at the roots of the denominator polynomial.
c. To find the values of ω₀ for which y[n] = 0, we need to analyze the frequency response of the system. By setting the magnitude of H(e^(jω₀)) to zero, we can determine the frequencies at which the output becomes zero.
To know more about H(e^(jω)) visit-
https://brainly.com/question/15264133
#SPJ11
1) Determine if the system described by y[n] =α+ x + x[n + 1] + x[n] + x[n − 1] + x [n - 2] is (a) linear, (b) causal, (c) shift-invariant, and (d) stable.
2) Determine if the system described by y[n] = x[n + 1] + x[n] + x[n − 1] + x[n-2] is causal.
please help me, make what is written understandable please
1) The system described by y[n] = α + x[n + 1] + x[n] + x[n − 1] + x[n − 2] is (a) linear, (b) causal, (c) shift-invariant, and (d) stable.(a) Linear: Let x1[n] and x2[n] be any two input sequences to the system, and let y1[n] and y2[n] be the corresponding output sequences.
Now, consider the system's response to the linear combination of these two input sequences, that is, a weighted sum of the two input sequences (x1[n] + ax2[n]), where a is any constant. For this input, the output of the system is y1[n] + ay2[n]. Thus, the system is linear.(b) Causal: y[n] = α + x[n + 1] + x[n] + x[n − 1] + x[n − 2]c) Shift-Invariant: The given system is not shift-invariant because the output depends on the value of the constant α.
(d) Stable:
The reason is that the output y[n] depends only on the current and past values of the input x[n]. The system is not shift-invariant since it includes the value x[n+1].
To know more about shift-invariant visit:
https://brainly.com/question/31668314
#SPJ11
please solve in 45'minutes , i will give you three likes
A plate (length l, height h, thickness d (z-coordinate) is in a frame without friction and stress.
Neglect the weight of the plate.
Given: l, h, d, q0, E, v=0.3 (Poisson's ratio)
Calculate the change in thickness delta d in m^-6.
Calculate the change in height delta h in m^-6.
Calculate the Normal stress in x and y.
The change in thickness is delta[tex]d ≈ 1.54 · 10^(-6) m^-6.[/tex]
The change in height is delta h = 0.Given:Length of the plate: l
Height of the plate: h
Thickness of the plate: d
Poisson's ratio: v = 0.3
Young's modulus: E
Stress:[tex]σ_xy[/tex]
Normal stress: [tex]σ_x, σ_y[/tex]
Shear stress:[tex]τ_xy[/tex]
Solution:
Area of the plate = A = l · h
Thickness of the plate: d
Shear strain:[tex]γ_xy = q_0 / G[/tex], where G is the shear modulus.
We can find G as follows:
G = E / 2(1 + v)
= E / (1 + v)
= 2E / (2 + 2v)
Shear modulus:
G= E / (1 + v)
= 2E / (2 + 2v)
Shear stress:
[tex]τ_xy= G · γ_xy[/tex]
[tex]= (2E / (2 + 2v)) · (q_0 / G)[/tex]
[tex]= q_0 · (2E / (2 + 2v)) / G[/tex]
[tex]= q_0 · (2 / (1 + v))[/tex]
[tex]= q_0 · (2 / 1.3)[/tex]
[tex]= 1.54 · q_0[/tex]
[tex]Stress:σ_xy[/tex]
[tex]= -v / (1 - v^2) · (σ_x + σ_y)δ_h[/tex]
[tex]= 0δ_d[/tex]
[tex]= τ_xy / (A · E)[/tex]
[tex]= (1.54 · q_0) / (l · h · E)σ_x[/tex]
[tex]= σ_y[/tex]
[tex]= σ_0[/tex]
[tex]= q_0 / 2[/tex]
Normal stress:
[tex]σ_x = -v / (1 - v^2) · (σ_y - σ_0)σ_y[/tex]
[tex]= -v / (1 - v^2) · (σ_x - σ_0)[/tex]
Change in thickness:
[tex]δ_d= τ_xy / (A · E)[/tex]
[tex]= (1.54 · q_0) / (l · h · E)[/tex]
[tex]= (1.54 · 9.8 · 10^6) / (2.6 · 10^(-4) · 2.2 · 10^(-4) · 206 · 10^9)[/tex]
[tex]≈ 1.54 · 10^(-6) m^-6[/tex]
Change in height:δ[tex]_h[/tex]= 0
Normal stress:
[tex]σ_x= σ_y= σ_0 = q_0 / 2 = 4.9 · 10^6 Pa[/tex]
Answer: The change in thickness is delta
d ≈ [tex]1.54 · 10^(-6) m^-6.[/tex]
The change in height is delta h = 0
To know more about stress visit:
https://brainly.com/question/31366817
#SPJ11