7. Determine the motion of the damped spring-mass system governed by the given initial-value problemdy+2dt2dy+ 5y = 0, y(0) = 0, y'(0) = 2dtand sketch the graph of the solution.

Answered: Image /qna-images/answer/3d5e3dbf-13b9-4433-93ca-7815fbd4c484.jpg

Answered: 7. Determine the motion of the damped…

7. Determine the motion of the damped spring-mass system governed by the given initial- value problem dy dy + 2- dt2 + 5y = 0, y(0) = 0, y'(0) = 2 dt

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A mass weighing 16 lb stretches a spring 1/4 feet. The mass is attached to a viscous damper with a damping constant of 2 lb-s/ft and is set in motion from its equilibrium position with a downward velocity of 1/2 ft/s. a) Set up the initial value problem (differential equation). b) Solve the equation to find the position of the mass y at any time t. c) Determine when the mass first returns to its equilibrium position. Assume that the y-axis is directed downward.
• Sheet no.2: Exercises/solve the following D.E using L.T. 1. y"+3y'+2y = c', y(0) = 1, y'(0) = 0,
(1 point) Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is 30 if 0 ≤t≤/2, F(t) 0 ift > π/2. a. Solve the initial value problem, using that the displacement y(t) and velocity y' (t) remain continuous when the applied force is discontinuous. For 0 ≤ts/2, y(t) Fortπ/2, y(t) = 0 (-3/8)(e^(-21))cos(6t)-(1/8)(e^(-2t))sin(6t)+3/8 help (formulas) help (formulas) b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. t-∞ For very large positive values of t, y(t) ≈0 help (formulas)
y(0) = 6
A spring mass system consists of a spring with spring constant k and an attached block of mass m is submerged in a liquid that produces a damping force Fr. m = 2 KG K = 36 N/m Fr 18 times the velocity of the center of mass of the block. = If the mass is initially released from rest 1m below the equilibrium position: Enter your answer in lower case, ex x"+ax'+bx=0 a. "The second degree equation that describe the motion of the center of mass of the attached block is b. The initial conditions are x(0)= c. The Arbitrary Constants that satisfy the IC's are C= the order does not matter" , x'(0)= C=
Solve by the method of: Inhomogeneous higher order linear y" - 6y' + 8y = sin(x)
2) Assume that the motion of a mass-spring system with damping is governed by d+b+8y = 0, y(0) = 1, y'(0) = 0. Find the equation of motion for b = 3.
y'= t2y - 4y / t+2 diferansiyel denklemin ayrılabilir olduğununu ve çözümünü gösteriniz
The motion of a mass-spring system with damping is governed by y"(t) + by' (t) + 64y(t) = 0; y(0) = 1, y' (0) = 0. Find the equation of motion and sketch its graph for b = 0, 10, 16, and 20.
Solve the IVP: d'y + 3 dy dt² dt +2y = 8(1-5)+ U(t-10), y(0) = 0, y' (0)= /
Suppose a mass spring system with damping is modeled by the IVP y+8y'+\by =0; ylos =2; y'CO) =-1 a) If you were to graph the equation of motion using a graphing that you will see on your screen. Calculator, which is the graph And why? ylt) (I) (1x) 21 2 (I1) (Iv) 2- t 2 2 b) which best deseribes this system? Explain why. mass spring (I) underdamped (II) overdanmped (m) critically damped (m) undam ped E) NONE
The motion of a mass-spring system with damping is governed by y''(t) + 8y'(t) + ky(t) = 0; y(0) = 2, and y'(0) = 0. Find the equation of motion and sketch its graph for k= 14, 16, and 18.