Question

A block rest on a horizontal table which is executing SHM in the horizontal with an amplitude $a$ if the coefficient of friction is $\mu$, then the block just start to slip when the frequency of oscillation is

• A. $\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$
• B. $2\pi \sqrt{\frac{a}{\mu g}}$
• C. $\frac{1}{2\pi }\sqrt{\frac{a}{\mu g}}$
• D. $\sqrt{\frac{a}{\mu g}}$

Answer 1

The correct option is A $\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$

The block will slip if the maximum force acting on the block during SHM is more than the limiting friction.

$F_{max}\ge F_{r,min}$

$m{\omega }^{2}a\ge \mu mg$

$\omega \ge \sqrt{\frac{\mu g}{a}}$

$f\ge \frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}$

Note that energy in SHM is conserved. However, in the given problem, friction is present which means energy will be lost in the form of heat. For the body to perform sustained oscillations, external force will be required. Hence, this is an example of forced oscillations.