I do not need to plot continuous curve, but I need to know the relative change in position between the base and the point mass at a given time.

m=100kg

damper coefficient c=variable

spring constant k=variable

constant acceleration a= 6g= 6x9.81m/s^2

time = 0.25s

my formula looks something like this

mx''+ cx' + kx = c*a*t + 1/2*k*a*t

^{2 }My particulate solution looks something like this: X

_{p}(t)=1/2*a*t

^{2}- m*a/k

This is pretty much as far as I have come. I do have a homogenous solution also, but it depends greatly on the value of k and c as you do know.

Could anyone help me to assess this?