Question

A mass $m$ is suspended from a massless pulley, which itself is suspended by a massless string and a spring as shown in figure. What will be the time period of oscillations of the mass? The force constant of spring is $K$.

• A. $2\pi \sqrt{\frac{m}{2K}}$
• B. $2\pi \sqrt{\frac{m}{K}}$
• C. $\pi \sqrt{\frac{m}{K}}$
• D. $\pi \sqrt{\frac{m}{2K}}$

Answer 1

The correct option is A $2\pi \sqrt{\frac{m}{2K}}$

Let extension in spring be $x$. Then tension in the string will be $Kx$

Tension in the string attached to the mass will be $2Kx$
Therefore, restoring force $F=2Kx=-K^{\prime }x$
And, $T=2\pi \sqrt{\frac{m}{K^{\prime }}}$
or, $T=2\pi \sqrt{\frac{m}{2K}}$