Question

A block of mass 100 g attached to a ring of stiffness 100 N/m is lying on a frictionless poor as shown. The block is moved to compress the ring by 10 cm and released. li the collision with the mil is elastic then find the time period of oscillations.

Answer 1

$s=10\sin wt$ $\sin wt=\frac{5}{10}=\frac{1}{2}$ $wt=\frac{\pi }{6}$

$\frac{2\pi }{T}t=\frac{\pi }{6}\Rightarrow t=\frac{T}{1^2}$

$T^{\prime }=\frac{T}{2}+2\times \frac{T}{12}=(\frac{1}{2}+\frac{1}{6})T$

$=\frac{4}{6}T=\frac{2}{3}T$

$=\frac{2}{3}\times 2\pi \sqrt{\frac{0.1}{100}}=\frac{4\pi }{30\sqrt{10}}=0.133\sec$