Two masses M1 and M2 are connected by a string constant k and are placed on a smooth horizontal surface.Initially the spring is stretched through a distance 'd' when the system is released from rest.find the distance moved by the two masses when the spring is compressed by a distance 'd'.

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Solution

When the spring is stretched through a distance d

The ratio of the distance moved by m1 to that of m2 is such that d1/ d2 = m2/ m1

This can be written as d1 /( d1 + d2) = m2/ ( m1 + m2)

d1 = m2d /( m1 + m2), Since x = d1+ d2

m1 again comes to rest when its distance moved is 2d1.

Hence, 2d1 = m2* 2d/ ( m1 + m2)

Similarly for the mass m2, distance moved is 2d2 = m1 * 2d / (m1 + m2)

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