I'm not sure what you mean with the eccentric mass "rotating about the center of this system".
Rotating around what? Around the 100 kg mass?
Do you have a schematic or drawing which explains what you are trying to achieve?
It sounds like you will have to use the planar mechanical library.
that was a good start; mass spring and damper for the compressor on its mount.
You are just missing an additional force input on that mass representing the (vertical) imbalance due to the rotating mass - using centrifugal force.
So the final model will look like this:
You can see the comparison of the mass displacement with the given solution, it matches both amplitude and phase.
Actually, instead of looking in time domain only, you can also use the "Linear Analysis mode" in Amesim to get to the solution.
Do a Bode plot at 0.5 sec (when the response is stabilized) between the force imbalance input amplitude (control variable) and the response of the mass displacement (observer variable).
Then check the amplitude and phase at 50 Hz - which is the imbalance excitation frequency here:
You see the phase is 4.0520 degree. The sign difference in the model is due to the fact that the force is positive going down and the mass displacement is positive going up. Ideally you would want to reverse the mass so the positive directions are both the same...
For the amplitude you see: 20 * log (¦F¦/¦x¦) = -138.9798
Here ¦F¦=986.044, so we get the expected amplitude ¦x¦=X=1.109966e-4