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  • Answer the following questions: (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations.

Q. 14.16 (b) Answer the following questions :

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations: For larger angles of oscillation, a more involved analysis shows that T is greater than   2\pi \sqrt{\frac{l}{g}}.   Think of a qualitative argument to appreciate this result.

                          

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In reaching the result T=2\pi \sqrt{\frac{l}{g}} we have assumed sin(x/l)=x/l. This assumption is only true for very small values of x (or\ \theta ). Therefore it is obvious that once x takes larger values we will have deviations from the above-mentioned value.

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