Frequency response of a spring mass damper system

[danbone87]

Consider a system with m = 100, c = 100 and k = 400. If y(t) = 3sin(1.5t), determine x(t) and ft(t).

I don't have a picture handy but the equations for the system turn out like this.

mx''+cx'+kx = cy' + ky

Transfer function = x/y = cy' + ky / mx'' + cx' + kx

then w/a laplace transform i get cs + k / ms^2 + cs + k

i replace the s' w/ (j * omega) and eventually reach the dimensionless form of the equation which is

X(s)/Y(s) = 1 + 2(zeta)(w/wn)j / (1-((w^2)/(wn^2))+ 2(zeta)(w/wn)j

I'm kinda lost from here. I don't think i understand what they're actually asking me to find. Does he want the magnitude of x(t) and ft(t) or what?

any kick in the right direction is appreciated

 

[Dr.D]

The problem statement said, "determine x(t) and ft(t)." These are real functions of time, not functions of the complex variable, s. That's what they said they want you to find.