Question

A system is shown in the figure. The time period for small oscillations of the two blocks will be.

• A. $2 \pi \sqrt{\frac{3 m}{k}}$
• B. $2 \pi \sqrt{\frac{3 m}{2 k}}$
• C. $2 \pi \sqrt{\frac{3 m}{4 k}}$
• D. $2 \pi \sqrt{\frac{3 m}{8 k}}$

Answer 1

Answer: (C)

Both the spring are in series
$\Rightarrow K_{e q}=\frac{K(2 K)}{K+2 K}=\frac{2 K}{3}$
Time period
$T=2 \pi \sqrt{\frac{\mu}{K_{e q}}} \text { where } \mu=\frac{m_{1} m_{2}}{m_{1}+m_{2}}$
Here $ \mu=\frac{m}{2}$
$\Rightarrow T=2 \pi \sqrt{\frac{m}{2} \cdot \frac{3}{2 K}}=2 \pi \sqrt{\frac{3 m}{4 K}}$