Base Excitation: Find response and transmitted force

[deerslayersh]

Homework Statement

The diagram simulates a vehicle driving on a rough road. Let v=constant. Find an equation for the response z(t) as well as the force transmitted to the vehicle

http://imgur.com/GUQcHx7

Homework Equations

x'' + 2ζω(x'-x_b') + ω^2(x-x_b) = 0
x_b(t) = X(iω)*e^(iωt)

The Attempt at a Solution

I'm confused at how to relate the equation y(x) to the time domain. We're given the curve the vehicle travels on with respect to x, but the response is with respect to time.

 

[deerslayersh]

I figured it out.