Question

Find the amplitude of oscillation if the masses make a perfectly inelastic collision and remain together on the spring. What is the period of oscillation?

Answer 1

$\omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{600}{2+1}}=10\sqrt{2}$ rad/s

$v_2^{\prime }=\left(\frac{m_2-m_1}{m_2+m_1}\right)v_2+\left(\frac{2m_1}{m_1+m_2}\right)v_1$
$=\left(\frac{2-1}{1+2}\right)\left(6\right)=2$ m/s

$\therefore$ $v=\omega A$

or $A=\frac{v}{\omega }=\frac{2}{10\sqrt{2}}$ m
$=0.141$ m$=14.1$ cm
$T=\frac{2\pi }{\omega }=\frac{2\pi }{10\sqrt{2}}=0.44$ s