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Harmonic Oscillations

There are a large variety of physical systems which perform a motion that regularly repeats itself in time and space. Any motion that repeats itself at definite interval of time, like the motion of earth around the Sun, is said to be periodic. A periodic motion which takes a system back and forth between extreme ends of a trajectory is said to be oscillatory. Typical examples of oscillatory motions are the motion of the bob of a simple pendulum, to the motion of a block attached to a spring.

The basic feature of an oscillating object is that the motion is started by displacing the object from its position of stable equilibrium. When such a displacement is made, a restoring force develops which brings the object back to its equilibrium position and moves to the other side. Restoring force again comes into play, finally stops and pulls the object back to equilibrium position. The process repeats and the object oscillates back and forth about its position of stable equilibrium.

If the restoring force is proportional to the displacement of the object from its equilibrium position, the resultant oscillatory motion is called simple harmonic. We know about many examples of simple harmonic motion, the most common being the small oscillations of a simple pendulum. We shall first discuss a few more examples of such ‘ideal’ harmonic motions. A ‘real’ harmonic oscillator finally stops due to damping effects of energy-discipating forces such as friction. The oscillating of such a real oscillator can be maintained by driving it with the help of external source of energy.