If length of oscillating simple pendulum is made ( 3 1 ) times at a place keeping amplitude same then its total energy will be

Question

If length of oscillating simple pendulum is made ( 3 1 ​ ) times at a place keeping amplitude same then its total energy will be

TestHub · Accepted Answer

Total energy of a simple pendulum is given by $E = \frac{1}{2} m ω^{2} A^{2}$

For a simple pendulum, $ω = \frac{g}{l}$

Substituting $ω^{2} = \frac{g}{l}$ , we get $E = \frac{1}{2} m (\frac{g}{l}) A^{2}$

Since mass $m$ , acceleration due to gravity $g$ , and linear amplitude $A$ are constant, $E \propto \frac{1}{l}$

Given $l^{'} = \frac{l}{3}$

Therefore, $E^{'} = 3 E$

The total energy becomes $3$ times.

Answer: $3$ times

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