Question

The time period of mass M when disturbed from its equilibrium position and for the system shown in the figure is:

• A. $2\pi \sqrt{\frac{M}{K}}$
• B. $2\pi \sqrt{\frac{M}{2K}}$
• C. $2\pi \sqrt{\frac{M}{4K}}$
• D. $2\pi \sqrt{\frac{4M}{K}}$

Answer 1

The correct option is C $2\pi \sqrt{\frac{M}{4K}}$

If the mass moves down by $l$ then the spring extends by $2l$ (because each side extends by $l$)
The force extending the spring is $F=T$ where $T=$ tension in the string.
here $2T=Mg$ or $T=\frac{Mg}{2}$
so, $F=\frac{Mg}{2}=2kl$ or $\frac{l}{g}=\frac{M}{4k}$
Time period $=2\pi \sqrt{\frac{l}{g}}=2\pi \sqrt{\frac{M}{4k}}$