Consider a mass- spring system with damping. Suppose the object has unit mass, the coefficient of friction
Fantastic news! We've Found the answer you've been seeking!
Question:
Consider a mass- spring system with damping. Suppose the object has unit mass, the coefficient of friction is b = 1 and the spring constant is k = 1/2. The differential equation describing this situation is
d 2 y /dt 2 + dy /dt +a1/2 y = 0
- Convert this 2 nd order DE into a first-order system in the variables y and v. plot its direction field using Bluffton and consider why solutions behave as they do in terms of the spring and damping constants.
- Solve the system and find the specific solution to it staring at y(0) = 1 , v(0) = 2. Note that y(t) is a solution to the 2 nd order DE.
- For your solution above, as t -> ± ∞ what values do y(t) and v(t) approach?
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
Posted Date: