Consider a mass-spring system governed by the second order differential equation of the form my" +ry' +ky = f(t). i) Suppose that you are considering free motion of the system (that is f(t)= 0). Assume that m = 1;r 10;k =16 and the initial conditions y(0) = 1 and y'(0) = 0. Find the motion of the system. Is the system underdamping or overdamping? Suppose, you want to design the system for critical damping, what value should you choose for k? ii) Suppose you are considering forced motion of the system with m 1;r 0; k = 16; f(t)= sin4t and y(0)= y'(0) = 0. Then what kind of solution do you expect. Discuss the solution. What will happen if you include the effects of damping force to this system?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Consider a mass-spring system governed by the second order differential equation of the
form my" +ry' +ky = f(t).
i) Suppose that you are considering free motion of the system (that is f(t) =0).
Assume that m 1;r 10;k =16 and the initial conditions y(0) = 1 and y'(0) = 0.
Find the motion of the system. Is the system underdamping or overdamping?
Suppose, you want to design the system for critical damping, what value should
you choose for k?
ii) Suppose you are considering forced motion of the system with m 1;r = 0; k = 16;
f(t)= sin4t and y(0)= y'(0) = 0. Then what kind of solution do you expect.
Discuss the solution. What will happen if you include the effects of damping force
to this system?
Transcribed Image Text:Consider a mass-spring system governed by the second order differential equation of the form my" +ry' +ky = f(t). i) Suppose that you are considering free motion of the system (that is f(t) =0). Assume that m 1;r 10;k =16 and the initial conditions y(0) = 1 and y'(0) = 0. Find the motion of the system. Is the system underdamping or overdamping? Suppose, you want to design the system for critical damping, what value should you choose for k? ii) Suppose you are considering forced motion of the system with m 1;r = 0; k = 16; f(t)= sin4t and y(0)= y'(0) = 0. Then what kind of solution do you expect. Discuss the solution. What will happen if you include the effects of damping force to this system?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,