Question

The friction coefficient between the two blocks shown in the figure is $\mu$ and the horizontal plane is smooth. If the system is slightly displaced and released, the time period $\left(T\right)$ will be :

• A. $T=\pi \sqrt{\frac{M+m}{k}}$
• B. $T=2\pi \sqrt{\frac{\mu M+m}{k}}$
• C. $T=2\pi \sqrt{\frac{M+\mu m}{k}}$
• D. $T=2\pi \sqrt{\frac{M+m}{\mu k}}$

Answer 1

The correct option is A $T=\pi \sqrt{\frac{M+m}{k}}$

For small amplitude the two blocks oscillate together The angular frequency is $\omega =\sqrt{\frac{k}{M+m}}$ and so the time period $T=2\pi \sqrt{\frac{M+m}{k}}$