# Forced vibrations w/ damping problem

1. Mar 10, 2005

### huk

A spring is stretched 6 inches by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec/ft and is acted on by an external force of 4cos(2t) lb.

a) Determine the steady-state response of this system
b) If the given mass is replaced by a mass m, determine the value of m for which the amplitude of the steady-state response is maximum.

I got part a but didnt get part b.... Im not sure where to start... can anyone tell me how to start it? or any tips?

ps the answer to a is U(t) = (8/901)(30cos(2t)+sin(2t)) ft

thanks

2. Mar 11, 2005

### Gokul43201

Staff Emeritus
Write the expression for U(t) in terms of m (do not substitute m=8 lb).

Find the amplitude A(m), to be half the difference between the minimal and maximal values of U(t). The minima and maxima can be found from dU(t)/dt = 0.

Maximize the amplitude by setting dA(m)/dm = 0.

3. Mar 11, 2005

### huk

I actually got it already. Sorry about it but thanks anyways. it was such a simple calculus problem.................