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.

 

[HalfLostAndSearching]

.

I would first like to commend you for attempting to understand and solve this problem. It shows a dedication to learning and a desire to improve your understanding of the subject matter.

To answer your question, part a of the problem is asking you to derive the equation for the single degree of freedom (SDOF) system, where x represents the displacement of the seat and y represents the displacement of the base. The equation you have written is correct, but I would suggest writing it in terms of acceleration (x'' and y'') instead of displacement. This will make it easier to solve for the unknown variables.

For part b, you are being asked to develop the step response equation for the SDOF system. This means that you need to derive the equation using the parameters given in the problem, such as the mass, spring constant, damping coefficient, and initial displacement. Once you have the equation, you can plug in the values and plot the graph to see the response of the system.

I hope this helps clarify the problem for you. If you are still having trouble, I suggest seeking help from your teacher or a tutor who can guide you through the steps and provide further explanation. Keep up the good work!