This is a modelling question relating to the swing in a simple pendulum. A parti

Question

This is a modelling question relating to the swing in a simple pendulum.

A particle of mass m = 2.78 kg is suspended from a fixed point by a light inextensible string of length = 0.87 m. You are required to determine the relationship between the period of swing and the length of the pendulum. For small angle approximation, sin ? ? ?.

Calculate the period of the swing of this simple pendulum, in seconds, giving your answer to 3 decimal places. You may use g = 9.81 ms-2 and ? = 3.142. Show working.

Explanation / Answer

Solution: At any instant, acceleration of the oscillating body will have a tangential component which can be expressed as maT = - mg sin ?. Minus sign appears because of the oppositely directed acceleration with respect to displacement.

Now, aT = l? where l is the length of the pendulum and ? the angular acceleration. Considering small angle approximation, sin ? ~ ?.

Therefore ml? = -mg? or, ? = -(g/l)? or, |?/?| = (l/g) or, T = 2?(?/?)1/2 or, T = 2?(l/g)1/2. So its independent of mass m and ? < 4

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