Simple Harmonic Motion Physics?

Question

A block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 3.2 Hz. The coefficient of static friction between block and surface is 0.40. How great can the amplitude of the SHM be if the block is not to slip along the surface?

Answer 1

The acceleration of the table must not exceed the coefficient of friction * g, or 0.4g. The sinusoidal acceleration is w^2 * displacement amplitude A, where w = 2pi*f, f=3.2. So the maximum A = 0.4g/(2pi*3.2)^2 (in whatever length unit g is expressed in).