Question

A $2kg$ block moving with $10m/s$ strikes a spring of constant ${\pi }^{2}N/m$ attached to $2kg$ block at rest kept on a smooth floor. Find the time for which rear moving block remains in contact with spring.

Answer 1

Consider a point on the spring at center of mass the time period of oscillation of both black is

$\Rightarrow T=2\pi \sqrt{\frac{\left(\frac{m_1{m}_2}{m_1+m_2}\right)}{k}}$

$=2\pi \sqrt{\frac{4}{{4\pi }^2}}$

$=\frac{2\pi }{\pi }$

$=2$

The block rear only remains in contact for half period of oscillation.

$\Rightarrow t=\frac{T}{2}=s.$

Hence, solved.