I expect the Modal analysis would give an error due to the hyperelastic material model. If you got modes out, maybe you don't have a hyperelastic material model assigned to the body?
You should just run Transient Structural as Erik suggested in this thread:
In the Step controls, turn off Time Integration to compute the static deflection of the structure during step 1, while the base is held with zero displacement.
In Step 2, turn on Time integration, but don't apply any motion of the base. This is needed to avoid assigning an initial velocity to the top mass, which would be the distance moved divided by the duration of step 1.
In Step 3, begin the motion of the base.