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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Physics - ExemplarDraw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.

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