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  4. A pendulum of length L swings from rest to rest n times in one second. The value of acceleration due to gravity is

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Q. A pendulum of length L swings from rest to rest n times in one second. The value of acceleration due to gravity is

Oscillations

Solution:

$T =2 \pi \sqrt{\frac{ l }{ g }}$
frequency $=\frac{n}{2} \Rightarrow T=\frac{2}{n}$,
As its given rest to rest as $n .$
$\frac{2}{n}=2 \pi \sqrt{\frac{1}{g}}$
$\therefore g=n^{2} \pi^{2} L$