a) For the following ODEs, find roots λ of their characteristics equation and determine the type of damping (overdamped, undamped, underdamped, critically damped). For undamped and underdamped cases, find their angular frequency and period (14 points)
i) y''+6 y'+10 y=0
ii) 4 y''+8 y'+3 y=0
iii) y''+8 y'+16 y=0
b) Find the general solution for the following ODE 16 y''+8 y'+y=0(6 points)
c) Find the particular solution of b) if y(0)=2 and y'(0)=2.5 .(5 points)
Homework Answers
Add Answer to:
For the following ODEs, find roots λ of their characteristics equation and determine the type of damping
A certain physical system is described by the 2nd-order ordinary differential equation +6-0. dt (a) Determine...
A certain physical system is described by the 2nd-order ordinary differential equation +6-0. dt (a) Determine the natural frequency, a, of the system (b) Determine the damping ratio, , of the system. (c) Classify the system as undamped, underdamped, critically damped or overdamped.
Please help! Problem 1. For each of the following SOLDECC, find the general solution and classify...
Please help!
Problem 1. For each of the following SOLDECC, find the general solution and classify the solution as overdamped, underdamped, or critically damped. y" +6y'+9y- 6. y"+2y' +y 0
1) Answer the following questions for harmonic oscillator with the given parameters and initial c...
1) Answer the following questions for harmonic oscillator with the given parameters and initial conditions Find the specific solution without converting to a linear system Convert to a linear system Find the eigenvalues and eigenvectors of the corresponding linear system Classify the oscillator (underdamped, overdamped, critically damped, undamped) (use technology to) Sketch the direction field and phase portrait Sketch the x(t)- and v(t)-graphs of the solution a. b. c. d. e. f. A) mass m-2, spring constant k 1, damping...
This is a differential equation result of 5. Physical spring-mass systems almost always have some damping...
This is a differential equation
result of 5. Physical spring-mass systems almost always have some damping friction, air resistance, or a physical damper, calleda dashpot Because damping is primarily a friction force, we assume it is proportional to the velocity of the mass and acts in the opposite direction. So the damping force is given by -bx' for some constant b>0.Again applying Newton's second law, the differential equation becomes mx" +bx'+kc = 0 .(1) as a Determine the auxiliary equation...
For the harmonic oscillator with mel, C=8, K:16 ; Xo = 5, Vo=4, do the following...
For the harmonic oscillator with mel, C=8, K:16 ; Xo = 5, Vo=4, do the following a. Find the position function x(t) and determine whether the motion is overdamped, critically damped or underdamped. b. Find the undamped (when c-0) position function ult) = Co Cos(wot-do)
® Consider a damped unforced mass-spring system with m 1, γ 2, and k 26. a) (2 points) Find if th...
solve d ,e , f, g
® Consider a damped unforced mass-spring system with m 1, γ 2, and k 26. a) (2 points) Find if this system is critically damped, underdamped, or overdamped. b) (4 points) Find the position u(t) of the mass at any time t if u(0)-6 and (0) 0. c) (4 points) Find the amplitude R and the phase angle δ for this motion and express u(t) in the form: u(t)-Rcos(wt -)e d) (2 points) Sketch...
A mass m is attached to both a spring (with given spring constant k) and a...
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
(24 points) Find the general solution to each of the following differential equations dy a) =...
(24 points) Find the general solution to each of the following differential equations dy a) = e)(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 17y = 0. Is this solution (i) undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
3. Write a program called VibratingSystem that does the following a. Takes the following as input...
This two problems go together
3. Write a program called VibratingSystem that does the following a. Takes the following as input i. Spring constant, k; ii. Mass under vibration, m; iii. Coefficient of viscous damping, c, iv. Initial position of the mass. xi, v. And initial velocity of the mass. vi b. If the values k or m are less than or equal to zero, ask for those variables again. c. Plot the results for t from 0 to 20...
Math 216 Homework WebHWI, PIUUIUM A mass with mass 7 is attached to a spring with...
Math 216 Homework WebHWI, PIUUIUM A mass with mass 7 is attached to a spring with spring constant 42 and a dashpot giving a damping 55. The mass is set in motion with initial position 6 and initial velocity 8. (All values are given in consistent units) Find the position function (t) = The motion is (select the correct description) A. underdamped B. overdamped C. critically damped 0 ). Finally find the undamped position function u(t) = Cocos(wist - 00)...
A certain physical system is described by the 2nd-order ordinary differential equation +6-0. dt (a) Determine the natural frequency, a, of the system (b) Determine the damping ratio, , of the system. (c) Classify the system as undamped, underdamped, critically damped or overdamped.
Please help!
Problem 1. For each of the following SOLDECC, find the general solution and classify the solution as overdamped, underdamped, or critically damped. y" +6y'+9y- 6. y"+2y' +y 0
1) Answer the following questions for harmonic oscillator with the given parameters and initial conditions Find the specific solution without converting to a linear system Convert to a linear system Find the eigenvalues and eigenvectors of the corresponding linear system Classify the oscillator (underdamped, overdamped, critically damped, undamped) (use technology to) Sketch the direction field and phase portrait Sketch the x(t)- and v(t)-graphs of the solution a. b. c. d. e. f. A) mass m-2, spring constant k 1, damping...
This is a differential equation
result of 5. Physical spring-mass systems almost always have some damping friction, air resistance, or a physical damper, calleda dashpot Because damping is primarily a friction force, we assume it is proportional to the velocity of the mass and acts in the opposite direction. So the damping force is given by -bx' for some constant b>0.Again applying Newton's second law, the differential equation becomes mx" +bx'+kc = 0 .(1) as a Determine the auxiliary equation...
For the harmonic oscillator with mel, C=8, K:16 ; Xo = 5, Vo=4, do the following a. Find the position function x(t) and determine whether the motion is overdamped, critically damped or underdamped. b. Find the undamped (when c-0) position function ult) = Co Cos(wot-do)
solve d ,e , f, g
® Consider a damped unforced mass-spring system with m 1, γ 2, and k 26. a) (2 points) Find if this system is critically damped, underdamped, or overdamped. b) (4 points) Find the position u(t) of the mass at any time t if u(0)-6 and (0) 0. c) (4 points) Find the amplitude R and the phase angle δ for this motion and express u(t) in the form: u(t)-Rcos(wt -)e d) (2 points) Sketch...
A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position X, and initial velocity vo Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e-pt cos (0,t-a). Also, find the undamped position function u(t) = Cocos (0,0+ - )...
(24 points) Find the general solution to each of the following differential equations dy a) = e)(x - 2). Over what interval is this solution valid? dx b) y" - 2y + y = (Hint use the method of variation of parameters) 1 + x2 c) y" - 8y' + 17y = 0. Is this solution (i) undamped, (ii) critically damped, (iii) under-damped, or (iv) over-damped?
This two problems go together
3. Write a program called VibratingSystem that does the following a. Takes the following as input i. Spring constant, k; ii. Mass under vibration, m; iii. Coefficient of viscous damping, c, iv. Initial position of the mass. xi, v. And initial velocity of the mass. vi b. If the values k or m are less than or equal to zero, ask for those variables again. c. Plot the results for t from 0 to 20...
Math 216 Homework WebHWI, PIUUIUM A mass with mass 7 is attached to a spring with spring constant 42 and a dashpot giving a damping 55. The mass is set in motion with initial position 6 and initial velocity 8. (All values are given in consistent units) Find the position function (t) = The motion is (select the correct description) A. underdamped B. overdamped C. critically damped 0 ). Finally find the undamped position function u(t) = Cocos(wist - 00)...
Most questions answered within 3 hours.
-
The free energy change for the following reaction at 25 °C, when
[Sn2+] = 1.17 M...
asked 34 minutes ago -
An MNE is this kind of industry when competition in one country
is essentially independent of...
asked 2 hours ago -
. For this set of questions, determine what
proportion of a normal distribution is located betweeneach...
asked 2 hours ago -
A college student is employed as a door-to-door newspaper
salesman. Historical data suggests that the student...
asked 3 hours ago -
MATLAB HW 11 problem using Switch Case and Input commands
Write a script file that calculates...
asked 3 hours ago -
Considering gravitational time dilation, calculate the time that
passes in Earth’s surface while 1 hour passes...
asked 4 hours ago -
Minitab Problem: Take the Lake Hume June rainfall data and find
use the processes outlined in...
asked 4 hours ago -
X Company is trying to decide whether to continue using old
equipment to make Product A...
asked 4 hours ago -
IN PYTHON ONLY !! Program 2: Re-work
program #5 (WeeklyHours) from the previous assignment such that...
asked 5 hours ago -
The average length of time between arrivals at a turnpike
toll-booth is 26 seconds. What is...
asked 7 hours ago -
(a) A piston at 6.1 atm contains a gas that occupies a volume of
3.5 L....
asked 8 hours ago -
Please answer true or false. Words
cannot be changed or added in to make it true...
asked 8 hours ago