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Time taken from displacement from mean position to $β$ and back to mean position=$t_{1}=2T $

where $T$ is the time period of the oscillation without the wall barrier.

Thus $t_{1}=21 ×2πgL =πgL $

Time taken to displace from mean position to $α$ can be found by:

$α=βsin(ωt)$

$α=βsin(ωt)$

$⟹t=ω1 sin_{−1}βα $

$=gL sin_{−1}βα $

Thus time taken to displace from mean position to $α$ and back to mean position = $t_{2}=2gL sin_{−1}βα $

Thus the time period of the oscillation = $t_{1}+t_{2}=gL [π+2sin_{−1}βα ]$

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