A block of mass $m$ rests on a horizontal platform undergoing SHM horizontally with amplitude $A$ an

Question

A block of mass $m$ rests on a horizontal platform undergoing SHM horizontally with amplitude $A$ and angular frequency $\omega$. What is the maximum amplitude allowed so the block does not slip? ($\mu$ is the coefficient of static friction)

Professor PC Thomas Classes · Answer

The maximum pseudo-force on the block is $m\omega^2 A$. This must be balanced by maximum static friction $\mu mg$. Equating them: $m\omega^2 A = \mu mg \implies A = \mu g / \omega^2$.