A block resting on the horizontal surface executes SHM in horizontal plane with amplitude A The frequency of oscillation for which the block just starts to slip is ($\mathrm{\mu }$ = coefficient of friction, g = gravitational acceleration)

When restoring force will become equal to the frictional force block will start to slip.
$\therefore$     Restoring force = Friction force

$\Rightarrow \mathrm{kA}=\mathrm{\mu mg}$                             $\left(\because {\mathrm{F}}_{\text{restoring }}=-\mathrm{kx}\right)$                …(i)

Now,    frequency, $\mathrm{f}=\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

From Eq. (i), we get

                              $\mathrm{f}=\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{\mu g}}{\mathrm{A}}}$