You need to draw the spring in the geometry editor (DesignModeler or SpaceClaim) as a spiral curve and assign a cross-section for the wire diameter.
In Mechanical, mesh that curve with beam elements. Apply a Fixed Support to one end and add a Point Mass to the other end.
You say you want to apply a lateral acceleration. Is that a constant acceleration or short duration acceleration that sets the oscillation in motion?
What do you want to know about the oscillation? If all you want to know is the frequency of oscillation, you would perform a Modal analysis.
If you want to know how far the spring/mass bends during the application of the acceleration pulse, then you would use Transient Structural analysis.
BTW, you posted in Explicit Dynamics, which is a specialized solver and the things I said above do not use that solver.