If we start taking into account the free body diagram, we then start damping motion of a body by means of this equation:
m * d^2 x/dt^2 + c* dx/dt + k* x = 0
free undamped motion is when (c =0)
therefore
50* d^2 x/dt^2 + 200* x = 0
w = omega = sqrt(k/m) = sqrt(200/50) = 2
Then
A*cos(w*t) + B*sin(w*t) = x
find A and B using intial conditions and you will get the rest that you need. Hope this helps
