# Homework Help: Driven Harmonic Sys. Displacement Amp.

1. Sep 9, 2011

1. The problem statement, all variables and given/known data
I need to find the steady state displacement amplitude for a driven harmonic system.

2. Relevant equations
mass (m) = .5kg
stiffness (s) = 100 N/m
mechanical resistance (Rm) = 1.4 kg/s
force (f) = 2cos5t

3. The attempt at a solution
What I know:
angular freq (w) = 5 rad/sec
magnitude of force (F) = 2N
necessary diff. eq.: m$\ddot{x}$ + Rm$\dot{x}$ + sx = Fexp(iwt)
complex displacement: x=$\frac{1}{iw}$$\frac{Fexp(iwt)}{Rm + j(wm-s/w)}$

I can ignore exp(iwt) because |exp(iwt)|=1.

So I need to find the magnitude of the complex displacement (while ignoring exp(iwt)) but I just don't remember how to deal with complex numbers. I've basically got all the values for what's in the complex equation I just don't know what to do with it!

Last edited: Sep 9, 2011