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Now restoring force acting on body can be given by

F = -mgsin$θ$ (from figure)

F = -mgsin$θ$ (from figure)

If $θ$ is small

F = -mg$θ$ ( $∵sinθ≈θ$)

F = -mg$θ$ ( $∵sinθ≈θ$)

Let P be any point an the path of pendulum and makes $∠OMP=θ$ which is small and arc OP be x (displacemebt) then

$θ=1OP =1X $

$⇒F=1−mgx $ ........(1)

$θ=1OP =1X $

$⇒F=1−mgx $ ........(1)

$⇒$ force $∝$ displacement and opposite in direction hence an SHM

Now this of form F = -kx...............(2)

$⇒$ k = mg/I (from (1) and (2)

$T=2πspringfactorinertialfactor $

$⇒$ k = mg/I (from (1) and (2)

$T=2πspringfactorinertialfactor $

$T=2πmg/1m $

$⇒T=2πg1 $

Solve any question of Oscillations with:-

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