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  4. A simple pendulum of length l has a maximum angular displacement θ The maximum kinetic energy of the bob is:

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Q. A simple pendulum of length $ l $ has a maximum angular displacement $ \theta $ The maximum kinetic energy of the bob is:

JIPMERJIPMER 2005Oscillations

Solution:

Here: length of pendulum $ =l $
image
maximum angular displacement $ =\theta $
mass of the bob $= m$
Now height of the bob at maximum angular displacement is
$ h=l-l\cos \theta =(1-\cos\theta ) $
Also at the end of the displacement kinetic energy of the bob = potential energy of the bob
$ =mgh=mgl\,(1-\cos \theta ) $