Two masses m_(1) and m_(2) are connected by a spring of force constant k and are placed on a 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 two masses before they again comes to rest.

Two masses m_(1) and m_(2) are connected by a spring of force constant

1.	Two masses m_(1) and m_(2) are connected by a spring of force constant k and are placed on a 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 two masses before they again comes to rest.
Answer» Solution : 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. `Deltax_(CM)=0`. Let mass `m_(1)` displaces by `Deltax_(1)` and `m_(2)` displaces by `Deltax_(2)`, then We have `Deltax_(1)+Deltax_(2)=2x_(0)`............`(i)` and `Deltax_(cm)=(m_(1)Deltax_(1)+m_(2)Deltax_(2))/(m_(1)+m_(2))` As `Deltax_(cm)=0` `:.(m_(1)Deltax_(1)+m_(2)Deltax_(2))/(m_(1)+m_(2))=0`.......`(ii)` After solving equation `(i)` & `(ii)`, we get `Deltax_(1)=(2m_(2)x_(0))/(m_(1)+m_(2))`, `Deltax_(2)=(2m_(1)x_(0))/(m_(1)+m_(2))`