Use a Transient Structural analysis. Below are the instructions for a very simple model that will solve quickly.

In SpaceClaim, Draw two co-linear lines along the X-axis, then create two Beams. The vertex between the beams is where you will attach a nonlinear spring to ground. On the Workbench Tab, click Share so the two Beams will be connected. Exit SpaceClaim.

In Mechanical, right click on Model and insert a Connections folder. In the Connections folder, create a Translation Joint to Ground and scope it to the vertex on the left end of the beam. Edit the Joint coordinate system to point vertically.

Now create a Spring to Ground and scope it to the vertex where you want contact. Type in the coordinates of the Reference (ground) end of the spring to give it a length and direction below the vertex. Enter a spring rate. Get the model running with a linear spring first. Later you will use a Command Object to overwrite the linear spring element with a nonlinear spring element that has a Gap capability.

Drag the Joint to the Transient Structural to create a Joint Load. Here is where you can create a sinusoidal formula. Make sure to put at least 20 points per cycle.

Under Analysis Settings, set the End Time for how many seconds you want. Set Large Deflection to On.  Set Auto Time Stepping to On and set the initial and minimum substeps to put 20 substeps per cycle.

Under Damping Controls, enter the appropriate damping constants.

Under Solution, insert a Directional Deformation result and set it for the Y axis.

When the solution finishes, you can copy the deformation out of the result Tabular Data and paste it into Excel or Matlab where you can discard the initial transient response and keep the steady-state response.