Consider the situations shown in fig (a) and (b) initially the spring is unstretched when the mass m is released from rest. Assuming no friction in the pulley find (a) the maximum stretch in the spring (b) stretch in the spring when the system is in equilibium.

Answer

`(a) y_(max)=((2mg)/k)and y_(eq)=(mg)/k,`
(b)`y_(max)=(mg)/k andy_(eq)=(mg)/(2k)`

Explanation

For maximum stretch loss in P.E. of mass = gain in elastic energy of the spring while for equilibium in
(a) `mg=T`
`mg=2T` Further in case
(a) stretch of spring = displacement of mass while in case
(b) stretch of spring `=2xx` displacement of mass.