So I feel as though I have the correct solution, but am not positive. My problem is as follows: A block of mass M is at rest with respect to a surface which oscillates horizontally with sinusoidal motion described by the equation x(t)=Asin(ωt). Find an expression for the minimum value of the coefficient of static friction between the block and surface so that the block does not slip as the surface oscillates. ALSO: If the block were to slip, where in the oscillation would this happen? I stated that if the block were to slip, it would be when x''(t) is at a maximum. The expression for x''(t) is -ω2Asin(ωt) and so when ωt=∏/2, the acceleration is at it's max, because the sine is at 1. And I set the kinetic force equal to this expression for acceleration times the mass of the block. Like so: Mgμk = -ω2A. I finished with μk = -ω2A / g Let me know if you feel as though I am correct. Thanks!