Question

A block rests on a horizontal table which is executing S.H.M. in the horizontal plane with an amplitude A. What will be the frequency of oscillation, the block will just start to slip? (Coefficient of friction = μ.)

Answer 1

Restoring force on the block

=mω²A = μmg

∴ Acceleration in the block =μg

Frequency of oscillation,

f = \(\frac{1}{2\pi}\sqrt{\frac{Acceleration}{Displacement}}\)

= \(\frac{1}{2\pi}\sqrt{\frac{\mu g}{y}}\)