Q

# 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.

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.