Question

Consider the situation shown in figure. If the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. The time period is

• A. $2 \pi \sqrt{\frac{m}{k}}$
• B. $2 \pi \sqrt{\frac{m}{2 k}}$
• C. $2 \pi \sqrt{\frac{m}{5 k}}$
• D. $2 \pi \sqrt{\frac{2 m}{3 k}}$

Answer 1

Answer: (D)

When two masses oscillate as shown, the effective
mass is taken as $\mu$ (reduced mass) $=\frac{m_{1} m_{2}}{m_{1}+m_{2}}$
Here, $\mu=\frac{2 m \cdot m}{2 m+m}=\frac{2}{3} \,m$
Time period, $T=2 \pi \sqrt{\frac{\mu}{k}}=2 \pi \sqrt{\frac{2 m}{3 k}}$