100 Points!!!
y(t) = distance of weight from equilibrium position

ω= angular frequency (measured in radians per second)

A = amplitude

Ø= phase (depends on initial conditions)

c1 = A sin

c2 = A cos


Prove that: Asin(ωt+Ø)=c2sinωt+c1cosωt


Note: c1 and c2 are actually with the number slightly below the letter, if that makes sense. It wouldn't let me type it that way. Anyway, if anyone can help I would really appreciate it! Thank you!

Answers

Answer 1

Answer:

An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as

x(t) = x0 + A cos(ωt + φ).

The object oscillates about the equilibrium position x0.  If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by

x(t) = A cos(ωt + φ).

A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.  Simple harmonic motion is repetitive.  The period T is the time it takes the object to complete one oscillation and return to the starting position.  The angular frequency ω is given by ω = 2π/T.  The angular frequency is measured in radians per second.  The inverse of the period is the frequency f = 1/T.  The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time.  It is measured in units of Hertz, (1 Hz = 1/s).

The velocity of the object as a function of time is given by

v(t) = dx(t)/dt = -ω A sin(ωt + φ),

and the acceleration is given by

a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.


Related Questions

can someone solve a - 3 over 7 s = -8


and a + 24 = -15

STEP BY STEP PLEASE.

Answers

Answer:

a=-39; s=0.75

Step-by-step explanation:

Solve the System of Equations by Substitution.

First, solve one of the equations for a variable. I'll do the 2nd one because it only has one variable.

a+24=-15 -------> a=-39

Now we know what a is just plug it back into the other equation and get s.

[tex]\frac{a-3}{7s} =-8[/tex]

[tex]\frac{-39-3}{7s} =-8[/tex]

[tex]\frac{-42}{7s} =-8[/tex]

Switch the -8 and 7s

[tex]\frac{-42}{-8} =7s[/tex]

Simplify the fraction

5.25=7s

Divide by 7 to isolate the s

0.75=s

 

Answer:

2)a+24=-15

a=-15-24

a=-39

Step-by-step explanation:

What is the solution of 52(4m+3)−(1−2m)=72[3(3+2m)−(3−m)] ?

Answers

Answer:

56cm -x=43

Step-by-step explanation:

Please help me ASAP!!! and please explain it because I do not understand how to do this at all.

Answers

Answer:

The 3 one

Step-by-step explanation:

So first you need to find all the angles.

Triangles all have a total degree of 180.

Then you can start doing trig. To find c I did (4sqrt3)cos60 that equals 3.464 which is 2sqrt3. Then I figured out a by doing the same thing but with sine. (4sqrt3)sin60 and that equals 6. Then I moved to the other triangle. I figured out d next. 6tan45° and that equals 6. Then I did b by doing 6/cos45 and I got 6sqrt2

Median of 40,2,31,15,29,16 and X is 21. then X= ?​

Answers

Answer:

Let us arrange this data in ascending order.

2, 15, 16, 29, 31, 40.

x has to be in the middle if it is the median.

So it becomes 2, 15, 16, x, 29, 31, 40.

There are seven numbers. The median is the 4th one.

The median is given as 21.

So x = 21.

HOPE IT HELPS YOU, PLS MARK IT AS THE BRAINLIEST :D

How can you write the equation for a linear function if you know only two ordered pairs for the function?
Drag tiles to complete the explanation. Tiles may be used once, more than once, or not at all.

Answers

Answer: m

one set of ordered pair

b

(In that order)

Step-by-step explanation: Took the test just now, your welcome.

Mrs. Nelson deposits $2,500 in an account that earns 5% simple interest. How much is Mrs. Nelson's investment worth after 20 years ?
A:2500
B:5000
C:4500

Answers

The answer is B because 5% of 2500 is 125 so each year 125$ gets added to her account so you multiply 125 by 20 and you get 2500. Finally you add 2500 + 2500 which gives you 5000

300/3x6
A,580
B.600
C601
D620

Answers

Answer:

B. 600

Step-by-step explanation:

300 / 3 = 100

100 x 6 = 600

2x + 3 = x -4
what is the answer ​

Answers

Answer:

Step 1: Subtract x from both sides.

2x+3−x=x−4−x

x+3=−4

Step 2: Subtract 3 from both sides.

x+3−3=−4−3

x=−7

Answer:

x=−7

I need help with the question in the attached image.

Answers

Answer:

Third choice

Step-by-step explanation:

We can subtract 4r by r, and that gives 3r. 3 subtracted by negative 3 gives 6 (Remember, 2 negatives is a positive!). This gives 3r+6

Brainlyp pls!

which is equivalent to √3/√8 when denominator is "rationalized"?

Answers

Step-by-step explanation:

[tex]\dfrac{\sqrt3}{\sqrt8}=\dfrac{\sqrt3\cdot\sqrt2}{\sqrt8\cdot\sqrt2}=\dfrac{\sqrt{3\cdot2}}{\sqrt{8\cdot2}}=\dfrac{\sqrt6}{\sqrt{16}}=\dfrac{\sqrt6}{4}[/tex]

Used:

[tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16[/tex]

Create an expression that would represent the area of the triangle

Answers

Answer:

96cm

Step-by-step explanation:

A=1/2bxh (Area=BasexHeight) is the formula to find it.

A=1/2x192

A=96

Solve the inequality.
n - 21 > 16

Answers

Answer: N>37 or (37,♾)
Why:cause I’m pretty sure it should be that

Answer:

n>37

Move all all terms not containing n to the side of the inequality.

a scientist is studying the growth of bacteria the bacteria double every 20 min if there are 5 bacteria at the beginning how many bacteria will be there in 2 hours?

Answers

Answer:

15,625

Step-by-step explanation:

2h=120m

120/20 = 6

5^6 = 15,625

There are 15 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?

Answers

Answer:

12 Men

Step-by-step explanation:

Since the ratio is 4:5 (men:women) 15/5 = 3, so you use 3 as your multiplier and write 3 x 4 = 12 :D

I need help! 6th grade math! ASAP! Only 1 and 3. 10 Points each!

Answers

Answer:

1. (0,5) (16,21) (20,25) (36,41) (55,60)

Step-by-step explanation:

Hope this helped you!! Give brainliest

Answer:

nnrrharthtghgdzhgdhth

Step-by-step explanation:

15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:

Answers

Answer:

a

Step-by-step explanation:

Nick is saving up for a laptop. His dad gave him $50 to start a savings account. He earns $9 every hour from his job, which he also saves. Write the equation of a function that can be used to find y, the total Nick has saved after x hours.

fill in the blanks
y =__ x + __

Answers

Y=9x+50



50 is what he dad gave him that doesn’t change, we know he works and earns $9 but we don’t know how many hours

Plsss help meeeeeeeeeeeee

Answers

Answer:

x = 8

y = 14

Step-by-step explanation:

It's given in the question,

ΔABC ≅ ΔDEF

Therefore, by the property of congruence,

EF = BC, AB = ED and AC = FD

And m∠E = m∠B

Since, m∠E = m∠B

(6y - 4) = 80

6y = 80 + 4

6y = 84

y = 14

Since, AB = ED

10 = 3x - y

10 = 3x - 14

3x = 24

x = 8

The measures of the angles of a triangle are shown in the figure below. Solve
for x.

Answers

Answer:

[tex]x = 46[/tex]

Step-by-step explanation:

Given

The three angles in the triangle are: x, 34 and 100

Required

Determine the value of x

Angles in a triangle add up to 180.

So, we have:

[tex]x + 34 + 100 = 180[/tex]

[tex]x + 134 = 180[/tex]

Subtract 134 from both sides

[tex]x + 134 - 134 = 180 - 134[/tex]

[tex]x = 180 - 134[/tex]

[tex]x = 46[/tex]

Hence, the measure of x is 46

PLZZ HELP ASAAP LIKE I NEED THE ANSWER NOW, WILL MARK BRAINLEST

The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are
(2, 6)
(−2, 6)
(−2, −6)
(2, −6)

Answers

Answer:

(-2,-6)

Step-by-step explanation:

The length and width of the rectangle is 60 and 40. If the scale factor is ¼, what are the new measurements?

Answers

Answer:

15 and 10

Step-by-step explanation:

I hope this helps :)

how to factor this completely?
25v3 - 40v2 + 35v – 56​

Answers

Answer:

Factor 25v3−40v2+35v−56

25v3−40v2+35v−56

=(5v−8)(5v2+7)

Answer:

(5v−8)(5v2+7)

Solve using the quadratic formula x^2-12x+5=0

Answers

Answer:

x=6+[tex]\sqrt{x}[/tex]31

Evaluate f(x)=x+6 when x=−2,0, and 5.

Answers

Answer:

1. 4

2. 6

3. 11

Step-by-step explanation:

Plug each number into the equation (in place of x) to get the answer.

1. f(-2) = -2+6 = 4

2. f(0) = 0+6 = 6

3. f(5) = 5+6 = 11

Answer I will cashapp you!!!

Answers

Answer:

should be y= 4x + 24 let me know if it was wrong

Which input value produces the same output value for
the two functions?
O x=-12
O x=9
O x=-6
Ox=-3

Answers

Answer:

-6

Step-by-step explanation:

Took test

At x = -6, both functions have the same output of 3.

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, We get;

f(x) = 2/3x + 7

when x = -12;            

     = 2/3(-12) + 7                                      

     = -8 + 7                                            

     = -1                                                    

g(x) = 2x + 15....

when x = -12

= 2(-12) + 15

= -24 + 15

= - 9

When x = -9;                      

f(x) = 2/3(-9) + 7                              g(x) = 2(-9) + 15

     = -6 + 7                                             = -18 + 15

     = 1                                                     = -3

When x = -6;

f(x) = 2/3(-6) + 7                             g(x) = 2(-6) + 15

     = -4 + 7                                            = -12 + 15

     = 3                                                   = 3

Thus, At x = -6, both functions have the same output of 3.

Learn more about the function visit:

https://brainly.com/question/11624077

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If a two story home has a ground floor of 25*30 feet and second floor of 20*30 feet, what is the total square footage of the home?

Answers

Answer: 1350 ft^2

Step-by-step explanation:

The total square footage of the home will be equal to the sum of the areas of each floor.

We know that the ground floor is 25 ft by 30ft,  which can be thought of as a rectangle with a length of 25ft and a width of 30 ft.

We know that te area of a rectangle of width W and length L is:

A = L*W

then the area of the ground floor is:

A = 25ft*30ft = 750 ft^2

And the second floor is 20ft by 30ft, then using the same approach as above, the area of the second floor will be:

A = 20ft*30ft = 600ft^2

Then the total square footage of the home is:

SF = 750ft^2 + 600ft^2 = 1350 ft^2

The total square footage of the home will be 1350 feet².

Based on the information given, the area of the first floor will be:

= 25 × 30

= 750 feet²

The area of the second floor will be;

= 20 × 30

= 600 feet ²

The total square footage will be:

= 750 + 600

= 1350 feet ²

Read related link on:

https://brainly.com/question/20360160

What is the polar form of (x + 3)2 + y2 = 9?

r = −6 cos(θ)
r = −3 cos(θ)
r = 3 cos(θ)
r = 6 cos(θ)

Answers

Answer:

r = -6 cos(θ)

Step-by-step explanation:

got it right on edge

The equation (x + 3)² + y² = 9 into polar form is r = -6 cos(θ). The correct answer would be option (A).

What is the polar form?

The polar form of a complex number is given by r(cos(θ) + i sin(θ)), where r is the distance from the origin and θ is the angle formed by the point and the positive x-axis.

To convert the equation (x + 3)² + y² = 9 into polar form, we can complete the square on the x and y terms:

(x + 3)² + y² = (x² + 6x + 9) + y² = 9

Then we can express x and y in terms of r and θ:

x = r cos(θ) , y = r sin(θ)

Substituting these values into the equation and simplifying:

r² cos²(θ) + 6r cos(θ) + r² sin²(θ) = 9

r²(cos²(θ) + sin²(θ)) + 6r cos(θ) = 0

r² + 6r cos(θ) = 0

r(r + 6cos(θ)) = 0

Since r ≠ 0

So, the polar form of the equation is:

r = -6cos(θ)

Thus, the correct answer would be an option (A).

To learn more about the Polar Coordinates click here:

https://brainly.com/question/614180

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What is the length of x in the diagram below?

A triangle with vertical bisector forms 2 triangles with a right angle. One triangle has a side length of 5 and another angle with a measure 45 degrees. Another triangle has a hypotenuse with length x and another angle with measure 30 degrees.
StartFraction 5 Over StartRoot 3 EndRoot
StartFraction 10 Over StartRoot 3 EndRoot EndFraction
5 StartRoot 3 EndRoot
10

Answers

Answer:

That is a 45-45-90 triangle next to a 30-60-90 triangle.  

So, the height of the left triangle equals 5.

That makes the short side of the 30-60-90 triangle also equal to 5.

In a 30-60-90 triangle, the hypotenuse (or "x") is exactly twice the length of the shortest side.

Therefore, the hypotenuse (or "x") equals 10.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

edge 2020

Write the first five terms in the arithmetic sequence. f(n + 1) = f(n) – 19, f(1) = 34

Answers

Answer:

34, 15, -4, -23 and -42

Step-by-step explanation:

We are to find the first five sequence

when n = 1

f(2) = f(1) - 19

f(2) = 34 - 19

f(2) = 15

when n = 2

f(2+1) = f(2) - 19

f(3) = f(2) - 19

f(3) = 15 - 19

f(3) = -4

when n = 3

f(3+1) = f(3) - 19

f(4) = f(3) - 19

f(4) = -4 - 19

f(4) = -23

when n = 4

f(4+1) = f(4) - 19

f(5) = f(4) - 19

f(5) = -23 - 19

f(5) = -42

Hence the first five terms  in the arithmetic sequence are 34, 15, -4, -23 and -42

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