Question

Two masses m1 and m2 are connected by a spring of force constant K and is placed on a friction less 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

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Answer 2

It is given that two blocks of masses m1 and m2 are connected with a spring having spring constant k.
Initially the spring is stretched by a distance x0.

For the block to come to rest again,
Let the distance travelled by m1 be x1(towards right), and that travelled by m2 be x2towards left.

As no external force acts in horizontal direction, we can write:
m1x1 = m2x2    ...(1)

As the energy is conserved in the spring, we get:
 (12)kx20 = (12)k(x1+x2−x0)2⇒ x0 = x1+x2−x0⇒ x1+x2 = 2x0       ... (2)



∴ x1 = 2x0−x2Putting this value in equation (1), we get:m1(2x0−x0) = m2x2⇒2m1x0 − m1x2 = m2x2⇒x2 = 2m2m1+m2x0Similarly, x1 = (2m2m1+m2)x0