Help with a SDOF system, spring and base?

[lupinpooter]

Homework Statement

Homework Equations

Maybe the step response equation?

The Attempt at a Solution

I don't really understand the difference between a and b, but he said part a was supposed to be quite easy. Is a just:
mx'' = -k(x-y) - c(x' - y')
or something along those lines? where x represents the displacement of the seat, and y the displacement of the base, so y' = 4cm? or y = 4cm?

Using F₀= k * 0.04, and plugging the values into the step response equation, with zeta = c/2m*ω_n, and ω_n = √ (k/m), and ω_d= √(1-ζ²)ω_n, I got the graph at the bottom (I think), which makes me assume it's right, without much idea what I put for b. When it says 'develop', does this mean derive the step-response equation? Or just plug in the variables?

Any help would be appreciated. Thank you

 

[rude man]

Looks like you have the right equation for part a.

For part b you should input a step into y(t) at t=0 and solve the diff. equation for x(t). I would use the Laplace transform if you're familiar with it, otherwise you'd have to grind out the classical diff. eq.

I don't know if your "step response equation" is correct. It looks plausible. I would start from scratch rather than use it unless you get a strong indication that that's what's expected of you. What would you do with the tau in it?

 

[lupinpooter]

oh sorry, (t - tau) would just be t, taking tau=o as the moment that it steps

 

[rude man]

oh sorry, (t - tau) would just be t, taking tau=o as the moment that it steps

OK, so how about F₀? You don't know what that value is ...

Again, I suggest working with your part a equation.
I would let x=0 and y=0 when t<0.