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I suggest you use Transient Dynamics to track the time history of displacements of the masses with the initial condition of velocity on one mass.
While the springs may be linear, there are two ways for the Transient Dynamics to be solved.Â
One method assumes small displacements of the masses which means you can use a Modal Superposition method of solution which is a linear analysis. To use that, drop the Transient Structural analysis on the Solution cell of the Modal analysis.
The other method allows for large displacements which turns this into a nonlinear analysis and cannot use the Modal solution. To make this model, drop the Transient Structural analysis on the Model cell of the Modal analysis.