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A small mass is hung at the end of a light string of length 1.5 m...

A small mass is hung at the end of a light string of length 1.5 m and allowed to swing over a small amplitude as a simple pendulum. It is observed that the amplitude of swing is reduced to half its initial value in 30 complete swings. It may be assumed that the reduction of amplitude is due entirely to resistance of the air and this in turn may be assumed to be proportional to the velocity of the mass. Deduce in how many swings the amplitude would be reduced to half its initial value if the length of the pendulum were changed to 2 m.

First show that the equation of motion for this system is:

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