Q. Masses m and 3 m are attached to the two ends of a spring of constant k. If the system vibrates freely. The period of oscillation will be
A) $\pi\sqrt{\frac{m}{k}}$
B) $2\pi\sqrt{\frac{m}{k}}$
C) $\pi\sqrt{\frac{3m}{k}}$
D) $2\pi\sqrt{\frac{3m}{k}}$
Explanation
(c) Reduced mass of the system,
$\mu = \frac{m_{1}m_{2}}{m_{1} + m_{2}} = \frac{m \times 3m}{m + 3m} = \frac{3m}{4}$
Period of oscillation,
$T = 2\pi\sqrt{\frac{\mu}{k}} = 2\pi\sqrt{\frac{3m/4}{k}} = \pi\sqrt{\frac{3m}{k}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.