What is equivalent of C0 in mechanical system?
Whatever mounts are holding the force source, friction plate, or the wall (if made of real materials) can be elastically distorted and thus hold potential energy.  That’s just some of the parasitics that could contribute to the equivalent of C0.

If the force source is un-anchored and mass-less, then, with any applied force, it might launch off to the left at the speed of light, and the potential energy might be stored inside something like its wave function.