In the given diagram of a simple pendulum, the time taken by the bob to move from $ \mathrm{X} $ to $ \mathrm{Z} $ is ' $ \mathrm{t}_{1} $ ' and from $ \mathrm{Z} $ to $ \mathrm{O} $ is $ ^{\prime} \mathrm{t}_{2}^{\prime} $. Find the time period of this simple pendulum."

The time period of the given simple pendulum is the time taken by the bob to travel from $XZOYOZX$

Time taken by the bob from $X$ to $Z$ is $t_1$ and time taken by the bob from $Z$ to $O$ is $t_2$.

Therefore, total time taken by the bob to move from $X$ to $Y$ is $2( t_1+t_2)$.

And time taken to return from $Y$ to $X$ is also $2(t_1+t_2)$

Therefore, time period $=2(t_1+t_2)+2(t_1+t_2)$

$=4(t_1+t_2)$

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Updated on: 10-Oct-2022

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