Question

Two blocks each of mass $m$ is connected to the spring of spring constant $k$ as shown In the figure. If the blocks are displaced slightly In opposite directions and released, they will execute simple harmonic motion. The time period of oscillation is

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

Answer 1

Answer: (B)

$2\pi\sqrt{\frac{m}{2k}}$

Answer 2

Reduced mass of the system $\mu = \frac{\left(m\right)\left(m\right)}{m+m} = \frac{m}{2}$ $\therefore$ Time period, $T= 2\pi\sqrt{\frac{\mu}{k}}$ $= 2\pi\sqrt{\frac{m}{2k}}$