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What Makes a Simple Pendulum Oscillate?

Oscillating systems are ubiquitous. We come across them everywhere in physics. A simple harmonic oscillator system has a fixed point of equilibrium and keeps oscillating about this fixed point forever if left undisturbed. But what makes it oscillate at all? Why doesn't the system just rest at the equilibrium position, for the equilibrium point is nothing but a point of stability?  

The simple pendulum with an in extensible string, a bob at one end, tied at the other end, and under the influence of gravity is the first oscillator that we are generally introduced to. Though the physics guiding all oscillators is the same, we'll specifically visualize what makes the simple pendulum oscillate. 

Let the equilibrium position be the origin. When the pendulum is to the right of the origin, displacement is positive and when it is to the left, displacement is negative. When the pendulum is disturbed from the equilibrium point, a force tries to restore the system to the equilibrium position, because of gravity. This is the restoring force. 

Let the system be disturbed towards the right through a certain angle and released. Restoring force acts on the pendulum towards the left, trying to pull it back to the origin. Restoring force is directly proportional to the displacement. It decreases as the displacement decreases.

At the maximum displacement, the velocity is zero and the restoring force is maximum. As it is released and the bob comes towards the origin, the bob has a negative velocity. Restoring force and velocity are in the same direction. So velocity of the pendulum increases in it's journey to the origin.  

At the origin, the restoring force becomes zero. So should we expect the pendulum to come to rest? No, because though the restoring force is zero, it has a large negative velocity. Because of this inertia, the pendulum overshoots the equilibrium position and displaces towards the left.

This again produces a restoring force towards the right. So now the restoring force is trying to bring it towards the right and inertia of the negative velocity is moving it towards the left. The negative velocity gradually decreases and at a point becomes zero, where the restoring force takes over and the pendulum starts moving towards the origin again. Now there is an increasing positive velocity and due to its inertia, the bob overshoots the equilibrium point and takes the bob back to the right extreme displacement. The process repeats and the pendulum oscillates! 

So basically, restoring force brings it back to equilibrium from a disturbed position and inertia makes it overshoot the equilibrium and repeat the process. 

If there are no external damping agents like air resistance, the process can go on forever. But this of course is only an ideal or unreal situation. Practically, the pendulum will come to rest at the equilibrium position after some time. 

 

Image source: http://best-hypnosis-centers.com/2014/12/4-tips-on-how-to-choose-the-best-hypnosis-center/

Abhirami

Abhirami

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