Question

Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$, the time period for small oscillation is equal to

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

Answer 1

Answer: (D)

The reduced mass
$\mu=\frac{(m)(m)}{m+m}=\frac{m}{2}$
The given system is equivalent to a system of a particle of mass $m / 2$ connected to a spring of stiffness $k$ rigidly.
The required period of oscillation.
$T =2 \pi \sqrt{\frac{\mu}{k}}=2 \pi \sqrt{\frac{m / 2}{k}} $
$=\pi \sqrt{\frac{2 m}{k}}$