Dynamic phases in a spring-block system

Abstract

When a block is pulled via a spring across a surface, there appear to be several different dynamic ‘‘phases.’’ These can be characterized by the pulling velocity ${\mathit{v}}_0$ and a dynamic velocity ${\mathit{v}}_{\mathit{D}}$=g √m/k , where g is the acceleration of gravity, m is the mass of the block, and k is the spring constant. For sufficiently small ${\mathit{v}}_0$, the block displays stick-slip (relaxation) motion. Then, as a function of decreasing ${\mathit{v}}_{\mathit{D}}$, this stick-slip motion is first nearly periodic, then aperiodic with approximately an exponential slip size distribution, and then aperiodic with possibly a power-law slip size distribution. When ${\mathit{v}}_0$ is increased, the block eventually ceases to stick and just slides across the surface. The motion can then be adequately described by a Langevin model.