## Book: HC Verma - Concepts of Physics Part 1

### Chapter: 12. Simple Harmonic Motion

#### Subject: Physics - Class 11th

##### Q. No. 24 of Exercises

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24
##### Solve the previous problem if the pulley has a moment of inertia I about its axis and the string does not slip over it.

A simply method for solving this problem is energy method. Initial extension of the spring in the mean position is

During oscillation, at any position x below the equilibrium position, let the velocity of m be v and angular velocity of the pulley be . If r is the radius of the pull, then .

At any instant, total energy for the system executing SHM is constant. Therefore

Substitute the value of

Taking derivative of both sides with respect to t,

The above equation is a second order differential equation of a system executing SHM.

Therefore,

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