Could you solve this problem of vibration engineering

For a spring-mass system with base excitation, derive the following expression for the relative motion z(t) = x(t) – y(t), for an undamped system:

Now, assume that the base motion is specified by a velocity pulse of the base given by:

where U(t) is the Unit Step Function

 Consider that the velocity of the base has a jump from zero to v0 instantly at t=0.

Derive an expression for the acceleration for the base motion from the velocity equation above

 Derive an expression for z(t) using equation and the acceleration term you have calculated for the base

If the peak amplitude of z occurs at a t < t1, derive an expression for the maximum amplitude z.