Question

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \,N \,m^{-1}$ and the mass of the block is $2.0\, kg$. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass $1.0\, kg$ moving with a speed of $2.0/, ms^{-1}$ collides elastically with the first block. The collision is such that the $2.0\, kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.

Answer 1

$T=2 \pi \sqrt{\frac{m}{k}}=2 \pi sec$
Block returns to original position in $\frac{T}{2}=\pi sec$

$d=\frac{2}{3}(\pi)=\frac{2}{3}(3.14)=2.0933 \,m $
$ d=2.09 \,m$