Amplitude problem — Car shock absorbers going over a bump

[haruspex]

I did not consider speed of the car, it has to consider. I will ask him again.

No need to bother your prof again, I understand the question statement now.
First, solve the differential equation just for the car bouncing up and down on its springs. So this is damped (with unknown constant) but no forcing. (Or maybe you have a standard solution for that in your notes.)
Using that solution, figure out how much the amplitude reduces each period. You are told that it halves, so this allows you to find the damping constant.

Use the given velocity to find the forcing frequency.

 

[robax25]

the differential equation would be like that,
d²x/dt² +2Qωo dx/dt + ω²x=0 here Q=daming factor, Q= b/2√mk
b=daming constant kg/s

 

[haruspex]

the differential equation would be like that,
d²x/dt² +2Qωo dx/dt + ω²x=0 here Q=daming factor, Q= b/2√mk
b=daming constant kg/s

Ok. Can you use the information in the question about the halving and the equation at https://en.m.wikipedia.org/wiki/Damping_ratio#Logarithmic_decrement to find the damping ratio?