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
Could someone pls help me
Answers
A farmer watered 3/8 of a field. What percentage is equivalent to the fraction of the field the farmer watered?
Answers
Answer: 37.5%
Step-by-step explanation:
To find 3/8, divide 100 by 8 (12.5), then multiply that by 3 to figure out 3/8.
An item sells for $40. The sales tax on
the item is 8%. What is the sales tax and
total cost?
Answers
Answer:
$43.20 total
$3.20 sales tax
Explication:
40*1.08=43.2
Answer:
sales tax = $3.20
total cost = $43.20
Step-by-step explanation:
To calculate the sales tax on an item, multiply the price of the item by the tax percent in decimal form. To convert a percent to decimal form, divide the percent by (100).
Sales tax percent: 8%
In decimal form: 0.08
Multiply the sales tax in decimal form by the price of the item to find out the sales tax amount,
(item_price) * (sales_tax)
= (40) * (0.08)
= 3.2
Sales tax amount: $3.20
To find the total cost of the product, add the sales tax amount to the item price,
(item_price) + (sales_tax_amount)
= 40 + 3.20
= 43.20
Jed is building a roof for his shed. The highest point of the roof will be 3 ft higher than the top of the shed. The slanted roof will be 7 ft long. What is the measure of the angle formed by the top of the shed and the slanted roof?
Answers
Answer:
90 degrees
Step-by-step explanation:
Answer:
It’s 100% 25..
Step-by-step explanation:
When is subtraction always the first operation done in an expression?
Never
When it follows addition in an expression.
When it is the first operation in an expression, from left to right.
When it is in parentheses in an expression.
Answers
Answer:
When it is the first operation in an expression, from left to right.
help please triangles and trig
Answers
Given:
A figure of a right angle.
To find:
The value of x.
Solution:
We know that the measure of the altitude on the hypotenuse of a right right triangle is the geometric mean of the segments of the hypotenuse.
If the altitude "h", divides the hypotenuse in two segments "a" and "b", then
[tex]h=\sqrt{ab}[/tex]
In the given figure, the measure of the altitude is x and it divides the hypotenuse in two segments 3 units and 24 units.
Using the above theorem, we get
[tex]x=\sqrt{3\times 24}[/tex]
[tex]x=\sqrt{72}[/tex]
[tex]x=6\sqrt{2}[/tex]
Therefore, the required solutions for the given blanks are:
Blank 1: 72
Blank 2: 6
Blank 3: 2
A race is 6.75 kilometers long. What is the distance of this race in meters?
Answers
Answer:
6750 meters
Step-by-step explanation:
1 kilometer = 1000 meters
1000*6.75=6750
Answer:
6750 meters
Step-by-step explanation:
Kilometers are equal to 1000 meters, so we can just multiply 6.75 x 1000 to get 6750 meters
NEED HELP PLEASE ASAP! BRAINLIEST TO RIGHT ANSWER! Two similar rectangles have areas of 6 in.2 and 24 in.2. What is the scale factor of the smaller rectangle to the larger rectangle?
A. 2 : 1
B. 4 : 1
C. 6 : 1
Answers
When you divide 6/2 and 24/2 you get 4/1
Select all correct conversions.
0.6 km = 6,000 m
46 m = 4,600 cm
457 mm = 4.57 cm
7.5 m = 0.0075 km
0.31 m = 310 mm
Which ones are it?
Answers
Answer:
310 mm 0.6 km = 6,000 m 457 mm = 4.57 cmStep-by-step explanation:
The statements 46 m = 4,600 cm, 0.31 m = 310 mm, 7.5 m = 0.0075 km and 0.31 m = 310 mm are correct conversations
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that conversations 1km = 1000 m
1 cm = 10 mm
1 m = 100 cm
0.6 km = 6,000 m is not correct, as 0.6 km is 600m
46 m = 4,600 cm is correct.
0.31 m = 310 mm is correct
457 mm = 4.57 cm is incorrect, as 457 mm is 45.7 cm
7.5 m = 0.0075 km is correct
0.31 m = 310 mm is correct
Hence, the statements 46 m = 4,600 cm, 0.31 m = 310 mm, 7.5 m = 0.0075 km and 0.31 m = 310 mm are correct conversations
To learn more on Unit of Measurement click:
https://brainly.com/question/15402847
#SPJ2
Suppose you buy a CD for $300 that earns 3% APR and is compounded
quarterly. The CD matures in 5 years. Assume that if funds are withdrawn
before the CD matures, the early redemption fee is 3 months' interest. What is
the early redemption fee on this account?
A. $1.50
B. $6.00
C. $2.25
D. $3.75
Answers
The early redemption fee on this account is $2.25.
What is APR?The annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. APR is a number that shows the actual yearly cost of funds throughout the life of a loan or the revenue received on an investment. This includes any fees or additional costs linked with the transaction but excludes compounding. The APR provides consumers with a single number that they may use to compare lenders, credit cards, and investment products.
We buy a CD for $300 that earns 3% APR and is compounded quarterly.
So, The early withdrawal fee is equivalent to 3 months' interest.
= (APR / 12) X 3
= APR / 4
= 3% / 4
= 0.03/ 4
= 0.75
and, the Early withdrawal fee = 0.75 x $300
Thus, the redemption fee is
= 0.0075 x $300
= $2.25
learn more about interest here:
brainly.com/question/26164549
#SPJ7
someone help me please like mega pleaseee help a girl out
Answers
Answer:
B.
Step-by-step explanation:
about travels in the following path. How far north did it travel? Round your answer to the nearest 10th of a mile
Answers
Answer:
19.1 miles
Step-by-step explanation:
The situation given represents a right triangle.
Thus, we would use trigonometric function to find how far north the boat travelled.
Let's represent how far the boat travelled north with "x".
Thus:
Reference angle = 23°
Opposite = x
Adjacent = 45 miles
Apply TOA:
Tan 23° = Opp/Adj
Tan 23° = x/45
Multiply both sides by 45
45 × Tan 23° = x
x = 45 × Tan 23°
x = 19.1013667
x = 19.1 miles (nearest tenth of a mile)
12 = 0.005 X W
Solve the equation
Answers
The answer is W= 2400 bc you have to divide both sides.
Hope this helps!
Answer: look at the picture
Step-by-step explanation: Hope this help :D
EVERYBODY LOOK.
^^^^^^^^^^^^^^^^^^^
40 FREEPOINTS
Answers
Answer:
Oh ok add me abelthegoat8
Step-by-step explanation:
Answer:
I don't have sc, but thx for the points! :)
Step-by-step explanation:
have a good day!
Express 1/3 as a repeating decimal and round to the nearest hundredth.
Answers
Answer:
1/3 is .333... so you can write .33.... or .33 with a line on top of the 3's
Step-by-step explanation:
.3 is in the tenths and .33 is in the hundredths place
Newton yayınları anahtar kodu
Answers
Answer:
What does this even say maybe I can try and help.
literally a goat if someone gives me an answer for this please
Answers
Answer: D, 100
Step-by-step explanation:
Answer: 100 (D)
Step-by-step explanation:
cuz
What is the value of x in the equation (2x + 1)1/3 + 3 = 6
Answers
Answer:
x = 4
Step-by-step explanation:
Please only answer if you're 100% sure it's correct. Thank you. (It's pretty easy.)
Answers
Answer:
2x-7, 2x-7=14, 2+7
Step-by-step explanation:
I am 99% sure these are correct
Solve for x:
1.1.1
x² - 6x=0
Answers
Answer:
zoom in
mark me as brainliest
Separate the solutions and the quadratic equations are:
X=6,X=0
Directions: Find the perimeter and area of each figure below.
HELPPPP ASPPP
Answers
Answer:
17) [tex]6a^{3}b^{2}[/tex]
18) [tex]40m^{4} n^{10}[/tex]
19) 14x³y²
20) [tex]9x^{2} y^{6}[/tex]π
Step-by-step explanation:
17)
Area of triangle = 1/2*b*h
A = 1/2(4a²b)(3ab)
A = 6(a³b²)
18)
A = 1/2(4mn⁵)(20m³n⁵)
A = (40)(m⁴n¹⁰)
19)
A = 2 (1/2)(2xy)(3x²y)
A = (6x³y²) + (4x²y*2xy)
A = 6x³y² + 8x³y²
A = 14x³y²
20)
A = (3xy³)²
A = 3² x² (y³)²
10 points
question 5: a, b, and c.
Answers
Answer:
the First One By Adding Four
The Second One Add Five And Two
The Third Add Two And Substract Four
Choose all of the shapes that are used to create the net of a cylinder. circle triangle wedge rectangle
Answers
Answer:
trianglw
Step-by-step explanation:
Answer:
Two circles and a rectangle will make up a cylander.
Step-by-step explanation:
Have a good day! :)
The 98 percent confidence interval (−0.248,−0.134) was constructed to estimate the slope of a regression model for a bivariate data set with 20 values. Alice claims that a sample size of 25 will produce a narrower interval, all other things remaining the same. Desmond claims that a sample size of 15 will produce a narrower interval. Which statement is true about the claims made by Alice and Desmond?
a. Alice’s claim is correct.
b. Desmond’s claim is correct.
c. Both Alice’s claim and Desmond’s claim are correct.
d. Neither Alice’s claim nor Desmond’s claim is correct.
e. There is not enough information to determine whether the claims are correct.
Answers
Answer:
a. Alice’s claim is correct.
Step-by-step explanation:
Margin of error of a confidence interval:
The margin of error of a confidence interval is inversely proportional to the sample size. This means that a smaller sample size leads to a smaller margin of error and a narrower interval, while a larger sample size leads to a larger margin of error and a wider interval.
Alice claims that a sample size of 25 will produce a narrower interval
25 > 20, so smaller margin of error and narrower interval, which means that Alice is correct.
Desmond claims that a sample size of 15 will produce a narrower interval.
15 < 20, so larger margin of error and wider interval, which means that Desmond is wrong.
So the correct answer is given by option a.
The store sells 6 donuts for $15 Kim has $37.50 how many donuts can she buy?
Answers
Answer:
12 if the donuts are sold in boxes and not singular, 15 if you can buy a smaller sized box
Step-by-step explanation:
Hope this helps! have a great day!
6/15 = 2.50
37/2.50 = 15
(since 6 donuts are equal to 15 dollars you would need to divide 6 and 15 to get the original price ( which would be 2.50) and now that you have the original price you can divide the original price from the amount that she originally has to figure out how many donuts that she needs ( 37.50 / 2.50 = 15) which would leave kim to have 15 donuts
Tan x= sin x/cos X. Therefore tan (90-A) =
Answers
Answer:
tan (90° - A) = cot A
Step-by-step explanation:
tan (90° - A) = sin (90° - A) / cos (90° - A) = cos A / sin A = cot A
PLEASE HELP WITH NUMBER ONE or all of them will mark Brainly-est
Answers
Answer:
Step-by-step explanation:
Find m∠ECD
m∠B = __°
m∠ECD = __°
Answers
Answer:
Angle B= 31°
angle ECD=118°
Step-by-step explanation:
It Is Because Of The Two Sides Are Equal So that the opposite angle of each equal sides also equal.
angle A=angle B
31°=31°
So Angle B=31°
angle ACB+angle B+angle A=180°
angle ACB+31°+31°=180°
angle ACB+62°=180°
angle ACB=180°+62°
angle ACB=118°=angle ECD
Because It Is Him Opposite Angle
Answer this I’ll give brainalist + points, please help!
Answers
Answer:
B
Step-by-step explanation:
the mean of A
= (84 + 84 + 85 + 86) ÷ 4
= 339 ÷ 4
= 84.75
the median of A
= (84 + 85) ÷2
= 169 ÷ 2
= 84.5
84.75 > 84.5
the mean of B
= (74 + 79 + 82 + 87) ÷ 4
= 332 ÷ 4
= 80.5
the median of B
= (79 + 82) ÷2
= 161 ÷ 2
= 80.5
80.5 = 80.5
the mean = the median
the mean of C
= (63 + 66 + 67 + 68) ÷ 4
= 264 ÷ 4
= 66
the median of C
= (66 + 67) ÷2
= 133 ÷ 2
= 66.5
66 < 66.5
the mean of D
= (14 + 16 + 18 + 19) ÷ 4
= 67 ÷ 4
= 16.75
the median of D
= (16 + 18) ÷2
= 34 ÷ 2
= 17
16.75 > 17
Will the two expressions always be equivalent,
regardless of the value of p? Explain.
3(2p) and 2(3p)
Answers
Answer:
Yes
Step-by-step explanation:
If you multiply it out, the expressions have the same value of 6p, so whatever you plug in for p, it will always be the same