High frequency contact mechanics experiments were carried with a quartz crystal resonator, the surface of which was coated with a polystyrene film. The experiment is based on the ring-down of the resonator after the electrical excitation has been stopped. When a tip touches the quartz surface, the shear motion of the quartz is perturbed, which can be used to study force-displacement and force-speed relations in the contact zone. A nonlinear spring constant κl(x) and a nonlinear friction coefficient ξl(ẋ) are explicitly derived. When a ceramic sphere touches a polymer film the friction force depends more than linearly on lateral speed. This contrasts to metal-metal contacts or contacts between ceramic surfaces, where the friction force depends either linearly of sub-linearly on speed.