Question

A bullet of mass m strikes a block of mass M. The bullet remains embedded in the block. Find the amplitude of the resulting SHM.

Answer 1

Let v is speed of combined mass just after collision. Then from conservation of linear momentum, we have
$(M+m)v=m{v}_0$
$\therefore$ $v=\frac{m{v}_0}{M+m}$
This is maximum speed of combined mass at mean position
$\therefore$ $v=\omega A$
or $\left(\frac{m{v}_0}{M+m}\right)=\sqrt{\left(\frac{k}{M+m}\right)}A$ { $\because \omega =\frac{k}{m}$}
$\therefore$ $A=\frac{m{v}_0}{\sqrt{k(M+m)}}$