Two masses `m_1 and m_2` re connected by a spring of spring constant k and are placed on as frictionless horizontal surface. Initially the spring is stretched through a distance `x_0` when the system is released from rest. Find the distance moved by the two masses before they again come to rest.

Explanation

Blocks again come to rest when spring is compressed by `x_(0)`. Since no external force is acting on the system, so there is no change in the position of c.m. of the system i.e., `Delta x_(cm)=0`.
Let mass `m_(1)` displaces by `Delta x_(1)` and `m_(2)` displaces by `Delta x_(2)`, then
We have `Delta x_(1)+Delta x_(2)=2x_(0)` ...... (i)
and `Delta x_(cm)=(m_(1)Delta x_(1)+m_(2)Delta x_(2))/(m_(1)+m_(2))`
As `Delta x_(cm)=0 therefore (m_(1)Delta x_(1)+m_(2)Delta x_(2))/(m_(1)+m_(2))=0` ......(ii)
After solving equation (i) & (ii), we get
`Delta x_(1)=(2m_(2)x_(0))/(m_(1)+m_(2)), Delta x_(2)=(2m_(1)x_(0))/(m_(1)+m_(2))`