Consider harmonic oscillators with mass m, spring constant k, and damping coefficient b. For the values specified,
a. write the second-order differential equation and the corresponding first-order system.
b. find the eigenvalues and eigenvectors of the linear system.
c. classify the oscillator (as underdamped, overdamped, critically damped, or undamped) and, when appropriate, give the natural period.
d. sketch the phase portrait of the associated linear system and include the solution curve for the given initial condition.
Answers
Answer:
a) attached below
b) Eigen values : λ1 = -1 and λ2 = - 1/2
Eigenvector : V1 = - y1 and V2 = ( - 1/2 ) y2
c) since the Oscillator is > 0 hence it is Overdamped
Step-by-step explanation:
Lets take : m = 2 , k = 1 and b = 3
a) Second -order differential equation and the first order system
attached below
b) determine the eigenvalues and eigenvectors of the Linear system
Eigen values : λ1 = -1 and λ2 = - 1/2
Eigenvector : V1 = - y1 and V2 = ( - 1/2 ) y2
attached below is the detailed solution
c) The oscillator is classified as OVERDAMPED
To determine if the oscillator is damped, underdamped, or overdamped we will apply the relation below
b^2 - 4km
( 3 )^2 - 4(1)(2) = 1
since the Oscillator is > 0 hence it is Overdamped
d) Attached below is the phase portrait of the associated linear system
y(0) = 0
v(0) = 0
Related Questions
A baker uses 5 cups of flour to make 75 cookies. Using this same ratio, how many cups of flour will be needed for 45 cookies? Use the ratio table given to solve the problem.
Answers
Answer:
Since, the baker use 5cups for 75cookies.Then for 30 cookies number of cups=
=75/5
=15.
Therefore no. 1cups for 15cookies.so,for 30 cookies=
=15*2
=30.
So, 2cups are needed for 30cookies
A farmer used 204 feet of fencing to enclose a garden in the shape of a rectangle. If the length of the garden is twice the width, what is the width of the garden?
A) 34ft
B) 40.8ft
C) 51ft
D) 68ft
E) 81.6ft
Answers
Answer:
A
Step-by-step explanation:
Area=L+L+B+B
L=2
B=1
So, L+L+B+B=6
204/6=34
So, it's 34 ft, which is A.
What is the slope of the line that goes through (0,0) and (6, 3)?
Answers
Answer:
0.5
Step-by-step explanation:
so the slope is also known as the gradient in y=mx+c
Elijah bought a new car for $25,000. He paid
$5,000 up front and then $600 per month. How
many months will it take Elijah to pay off the car?
Answers
Answer: 6 days too be exact
Step-by-step explanation:
Answer:
33.333 months
Step-by-step explanation:
25,000-5,000=20,000
20,000/600=33.333
If he payed $5,000 upfront, the he only has $20,000 remaining to pay. If he is paying $600 a month then you divide the $20,000 by the $600 to 33.333 months. Hope this helps
Solve for x.
5(x + 1) = 4(X + 8)
Ox= 37
Ox=7
Ox=27
Ox=17
Help please
Answers
Answer:
27
Step-by-step explanation:
simplify 8x+7-x-4
help meeeeee!!!
Answers
Answer:
7x + 3
Step-by-step explanation:
Let's simplify step-by-step.
8x + 7 − x − 4
= 8x + 7 + −x + −4
Combine Like Terms:
= 8x + 7 + −x + −4
= (8x + −x) + (7 + −4)
= 7x + 3
Answer:
= 7x + 3
hope this helps and is right. p.s i really need brainliest :)
if my answer is wrong then I am incredibly sorry!
Choose all of the statements that correctly compare the two functions shown.
Alec's rate of savings is greater than Beth's.
entific
Alec and Beth are saving at the same rate.
Alec started with more money than Beth
mulas
Time
maining
:19:23
Beth started with more money than Alec,
de les
At 10 days, Alec will have $1 more than Beth in savings,
Answers
Answer:
b, c and e
Step-by-step explanation:
Given
See attachment for functions
Required
Select all statements that contain both functions
First, calculate the rate (slope) of both functions.
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Alec's
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (2,9)[/tex]
So, the slope is:
[tex]m = \frac{9 - 3}{2 - 0}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m =3[/tex]
For Beth's
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (12,38)[/tex]
So, the slope is:
[tex]m = \frac{38 - 17}{12 - 5}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m =3[/tex]
Beth and Rec have the same slope. Hence, they save at the same rate.
Next, determine the amount they started with.
This implies that we calculate y when x = 0
From Alec's graph.
[tex](x,y) = (0,3)[/tex]
Alec's initial savings is 3
For Beth's savings, we make use of slope formula.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
So, we have:
[tex]3 =\frac{y - 17}{0 - 5}[/tex]
[tex]3 =\frac{y - 17}{ - 5}[/tex]
[tex]y - 17 = -15[/tex]
[tex]y = 17 -15[/tex]
[tex]y = 2[/tex]
Beth's initial savings is 2
Hence, Alec started with more money
Next, is to determine who has more money after 10 days.
Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.
The difference (d) is calculated as:
[tex]d = 3 - 2[/tex]
[tex]d = 1[/tex]
Hence, Alec will have $1 more than Beth after 10 days
Answer:
its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.
Step-by-step explanation:
NEED HELP ASAP PLEASE! BRAINLIEST TO RIGHT ANSWER! Are the polygons similar? If they are, write a similarity statement and give the scale factor.
Answers
Answer:
B) Yes; POSN~KDAG; scale factor 5:4
Step-by-step explanation:
B) Yes; POSN~KDAG; scale factor 5:4
Same angles (If 3 are the same, the 4th is the same).
Comparing the 4 respective sides:
15/12=5/4
10/8=5/4
7.5/6=5/4
15/12=5/4
Find y.
1)6.76
2)7.54
3)18.55
4)29.83
Answers
9514 1404 393
Answer:
(c) 18.55
Step-by-step explanation:
The law of sines tells you ...
y/sin(106°) = 15/sin(51°)
y = 15×sin(106°)/sin(51°)
y ≈ 18.55
_____
The same kind of proportion can find x:
x = 15×sin(23°)/sin(51°)
x ≈ 7.54
Please note that the question posted here asks for the value of y. The value of x and the complete triangle solution are provided as a courtesy to those who may be asked for other values in this triangle.
Complete the square
to find the vertex
of this parabola.
y^2+4x - 2y+21=0
Answers
Answer:
::::::::::::::::::::
(-5,1)
The vertex of the parabola represented by the equation y² + 4x - 2y + 21 = 0 is (-5, 1).
The parabola is represented by the equation y² + 4x - 2y + 21 = 0.
Take the coefficient of y, which is -2, divide it by 2, and square the result:
(-2/2)² = 1
Now, we add and subtract this value inside the parentheses to maintain the equation's balance:
y² - 2y + 1 + 4x + 21 - 1 = 0
Rearranging the terms, we have:
(y² - 2y + 1) + 4x + 20 = 0
Now, the terms inside the parentheses can be written as a perfect square:
(y - 1)² + 4x + 20 = 0
Setting (y - 1)² = 0,
(y - 1)² = 0
y - 1 = 0
y = 1
Substitute y = 1 back into the equation to find the x-coordinate of the vertex:
(1 - 1)² + 4x + 20 = 0
0 + 4x + 20 = 0
4x = -20
x = -5
Therefore, the vertex of the parabola is (-5, 1).
Learn more about the parabola here:
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If x is an acute angle, and tan x=3/4
evaluate
COS x-sin x/COS x+ sin x
please answer fast 10 points and brainliest answer
Answers
Use the pic and solve the COS x-sin x/COS x+ sin x part
comment if there's something u don't understand
The value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
tanx = 3/4 (x is an acute angle)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}-1=\dfrac{4}{3}-1\\\\\rm \dfrac{cosx-sinx}{sinx}=\dfrac{1}{3}\\\\[/tex] ….(1)
[tex]\rm \dfrac{sinx}{cosx}=\dfrac{3}{4} \\\\\ \rm \dfrac{cosx}{sinx}+1=\dfrac{4}{3}+1\\\\\rm \dfrac{cosx+sinx}{sinx}=\dfrac{7}{3}\\\\[/tex] …(2)
Divide (1) ÷ (2)
(cosx-sinx)/(cosx+sinx) = (1/3)/(7/3) = 1/7
Thus, the value of (cosx-sinx)/(cosx+sinx) is 1/7 if the x is an acute angle, and tan x=3/4
Learn more about trigonometry here:
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The mean number of points in 1977 was 1189 points with standard deviation of 397 points. With a roughly normal distribution, what percent of performances would fall between 395 and 1983 points?
Your answer
A. 100%
B. 68%
C. 95%
D.99.7%
Answers
Answer:
C. 95%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1189 points, standard deviation of 397 points.
Percentage between 395 and 1983 points?
395 = 1189 - 2*397
1983 = 1189 + 2*397
So within 2 standard deviations of the mean, which by the Empirical Rule is approximately 95%, and the answer is option C.
Tell whether it is possible to draw a figure with the given description.
a triangle with sides of length 5 inches and 6 inches that meet at a 50° angle
Is it possible or not possible. Will give brinliest
Answers
Answer:
in my opinion it is not possibleStep-by-step explanation:
hope it helps you have a good day
Please help me ASAP really need help!!!
Answers
Answer:
2.7
Step-by-step explanation:
the scale factor should be consistant as you scale up and down. So you can divide 4.59 by its corresponding side of 1.7 in order to get the scale factor of 2.7. When repeated with the other sides this number should remian consitant.
In rectangle ABCD,If EC=13 find BD
Answers
Answer:
[tex]BD = 26\\[/tex]
Step-by-step explanation:
Given
[tex]EC = 13[/tex]
Required
Find [tex]BD[/tex]
In the given rectangle.
AC and BD are the diagonals.
This implies that:
[tex]AC = BD[/tex]
AC is calculated as:
[tex]AC = AE + EC[/tex]
Where
[tex]AE = EC[/tex]
So:
[tex]AC = EC + EC[/tex]
[tex]AC = 13+13[/tex]
[tex]AC = 26[/tex]
Recall that: [tex]AC = BD[/tex]
[tex]BD = 26\\[/tex]
A sample of bacteria is decaying according to the half-life model f(t) = Ne -0.226t, where N is the initial sample size and t
is time in hours. At t = 4, there are 25 bacteria remaining. What was the initial sample amount? Round your answer to the
nearest whole number, and do not include units.
Answers
Answer:
Step-by-step explanation:
A sample of bacteria is decaying according to the half-life model f(t) = Ne -0.226t, where N is the initial sample size and t
is time in hours. At t = 4, there are 25 bacteria remaining. What was the initial sample amount? Round your answer to the
nearest whole number, and do not include units.
If I apply distributive property to 6 (t + 12) = 114 then what operation will I need to use first
Answers
Answer:
Step-by-step explanation:
First divide 6 from the left size so it gets cancelled.
Basically 6 (t + 12) = 114 becomes (t + 12) = 114/6
Which becomes (t + 12) = 19
Now, (t + 12) - 12 = 19
Therefore, t = 19 - 12
Answer: t = 7
(whatever you do to one side, most be done to the other side too).
To check,
6(t+12)=114
6(7+12)=114
Solve brackets first, 6(19)=114
114=114
The first operation will be multiplying 6 with t and 6 with 12 and then adding both the terms also t is equal to 7.
What is Distributive property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
As per the given data:
To apply distributive property in 6 (t + 12) = 114
Distributive property: A (B + C) = A × B + A × C
Now for, 6 (t + 12) = 114
First operation will be multiplying 6 with t and 6 with 12 and then adding both the terms:
6 × t + 6 × 12 = 114
6t + 72 = 114
6t = 114 - 72
6t = 42
t = (42/6) = 7
Hence, the first operation will be multiplying 6 with t and 6 with 12 and then adding both the terms also t is equal to 7.
To learn more about Distributive property, click:
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Help please!!! I can’t figure it out
Answers
9514 1404 393
Answer:
C. ... 3 1/4 cups
Step-by-step explanation:
The problem statement tells you that the other measures are combined. That means you're looking for an expression like ...
3/8 × ((3 2/3) +(2 1/4) +(2 3/4))
This eliminates choices B and D.
If you look at the numbers in parentheses, you see that the 1/4 and 3/4 will have a sum of 1, so the only fraction in the sum will be 2/3. This eliminates choice A.
The only viable answer choice is C.
__
If you like, you can check to see that answer C is correct.
(3/8)(8 2/3) = (3/8)(26/3) = 26/8 = 3 2/8 = 3 1/4
i will be sooooo thankful if u helped me
Answers
Answer:
For 35 its C
Step-by-step explanation:
Solve 3y^3 + 12y^2 + 12y =0
Please
Answers
Answer:
y = 0, -2
Step-by-step explanation:
Factor out the common term 3y.
[tex]3y( {y}^{2} + 4y + 4) = 0[/tex]
Rewrite y² + 4y + 4 in the form of a² + 2ab + b², where a = y and b = 2.
[tex]3y( {y}^{2} + 2(y)(2) + {2}^{2} ) = 0[/tex]
Use square sum: (a + b)² = a² + 2ab + b².
[tex]3y(y + 2) ^{2} = 0[/tex]
solve for y.
y = 0, -2.
therefor, the answer for this equation is 0, - 2.
Please help me with this ASAP ASAP please please help
Answers
Answer:
Step-by-step explanation:
Base perimeter: 4 x 2 x π = 8π
LA = 8π x 6 = 48π
Base area = 4^2π = 16π
SA = 16π x 2 + 48π = 80π
V= 16π x 6 = 96π
PLEASE HELP!
I AM IN A HURRY
Answers
Answer:
Honestly I have no idea what is going on in this passage or whatever it is.
Step-by-step explanation:
How is the graph of the parent quadratic function transformed to produce the graph of y--(2x+6)2+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated
up 3 units
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated
up 3 units
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up
3 units
O The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up
3 units
Answers
Answer: a
Step-by-step explanation:
just took the test
reduce 12/20 to lowest term
Answers
Answer:
3/5
Step-by-step explanation:
12/20
(divide both by 2)
12/2= 6
20/2=10
6/10
(divide by both by 2)
6/2= 3
10/2= 5
3/5
What fraction is equivalent to 10 and has a denominator of 100? (2 points)
6
100
7
60
100
o
600
100
a
60
10
Answers
Answer:
1000 / 100
Step-by-step explanation:
Answer:
ff
Step-by-step explanation:
What is the mean for these numbers?
5,5,5,5
Answers
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT'S A COMPUTER PHONE AND TABLET VIRUS
Answer:
5
Step-by-step explanation:
What formula can be used to find circumference? Choose all that apply. *
Cat
2r
nd
2nd
Answers
Answer:
circumference =pi ×diameter
OR
pi × radius × 2
I apologize for the messy photo but please help me with this, I’m really confused! Thank you so so so much.
Answers
1)+4
2)-4
3) 2
4) i don't know
5)
Answer: (-2)²=4
-2²=-4
square root of 4 is 2
1 over the square root of 8 is -2
1 aquare root of -8 is 2,-2
Step-by-step explanation:plug them into calculator
$410 is invested in an account earning 4.2% interest (APR), compound quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answers
Pick the correct value for the image of A after applying the rotation matrix.
(- 3, -4)
(- 1, -4)
(1, -4)
(3, -4)
Answers
Answer:
A) (- 3, -4)
Step-by-step explanation:
edge 2021
Answer:
A) (-3, -4)
Step-by-step explanation: