Q. 22

When will the motion of a simple pendulum be simple harmonic?

Answer :

Forces acting on the pendulum,


Tension T due to the string


Force of gravity due to mass of pendulum in vertically downward direction, mg


Now the force of tension T is balanced by the cosine component of the weight, i.e.,



And the sine component of the weight is called the restoring force acting towards the equilibrium position of the pendulum


, now if θ is very small then, sin θ θ and we can write for θ ,


, where L is the length of the pendulum and is the tangential displacement.



Clearly F is proportional to the displacement and in opposite direction of tangential displacement


When the pendulum is displaced by a small angle θ such that the sin θ θ, then the pendulum will execute simple harmonic motion.


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