Question

two masses M1 and M2 are connected by a spring of force constant K and is placed on a frictionless horizontal surface. initially the spring is stretched through a distance x when the system is released from rest. find the distance moved by two masses before the again comes to rest

Answer 1

Distance stretched= x and x=x1+x2
Let the ratio of the distance be moved by m1 to that m2 be such that x1/x2=m2/m1

Also, x1/(x1+x2)=m2/(m1+m2)

~x1/x=m2/(m1+m2)
x1=m2x/(m1+m2)

m1 again comes to rest when it moves a distance of 2x1
~ 2x1 = m2*2x/(m1+m2)
Similarly for m2 , 2x2= m1*2x/(m1+m2)