Question

A block of mass m is attached from a spring of spring constant k and dropped from its natural length. Find the
amplitude of S.H.M.
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Answer 1

Given:

A block of mass m is attached from a spring of spring constant k.

It is dropped from its natural length.

To Find:

Amplitude of S.H.M.

Solution:

Here we want to find the maximum extension of the spring.

Lets analyse the mass movement.

Initially we drop it from a height, with 0 velocity.

Lets assume it has an extension A , when it reaches the lower most position, where its velocity becomes 0 and spring force dominates over the weight.

We can apply Work Energy theorem.

Change in Potential Energy = Kinetic energy of the spring+ Kinetic energy of the mass.

• mg( A) = 0.5kA² + 0
• A = 2mg/k

The  amplitude of S.H.M. is 2mg/k.