Question

Find the amplitude and period of oscillation if the collision is perfectly elastic?

Answer 1

If the collision is elastic,
${\omega }^{\prime }=\sqrt{\frac{600}{2}}=10\sqrt{3}$ rad/s
In elastic collision,
$v_2^{\prime }=\left(\frac{m_2-m_1}{m_2+m_1}\right)v_2+\left(\frac{2m_1}{m_1+m_2}\right)v_1$
$=\left(\frac{2\times 1}{1+2}\right)\left(6\right)=4$ m/s (As $v_2=0$)
This is maximum velocity.
$\therefore$ $v_2^{\prime }={\omega }^{\prime }{A}^{\prime }$
or $A^{\prime }=\frac{v_2^{\prime }}{{\omega }^{\prime }}=\frac{4}{10\sqrt{3}}=0.23$ m$=23$ cm
$T^{\prime }=\frac{2\pi }{{\omega }^{\prime }}=\frac{2\pi }{10\sqrt{3}}=0.36$ s