Question

Two identical particles each of mass 0.5 kg are interconnected by a light spring of stiffness 100 N/m, time period of small oscillation is

Answer 1

Given,

Mass, $M=0.5kg$

Spring constant, $k=100N{m}^{-3}$

The reduced mass, $\mu$

$\mu =\frac{\left(m\right)\left(m\right)}{(m+m)}=\frac{m}{2}$

The given system is equivalent to a of a particle of mass $\frac{m}{2}$ connected to a

Spring of stiffness rigidly. The required period of oscillation,

$T=2\pi \sqrt{\frac{\mu }{k}}=2\pi \sqrt{\frac{m/2}{k}}=\pi \sqrt{\frac{2m}{k}}$

$T=\pi \sqrt{\frac{2\times 0.5}{100}}=\frac{\pi }{10}\sec$

Hence, time period of oscillation is $\frac{\pi }{10}\sec$