Free Oscillations
Oscillation is a to and fro motion. If I jump up and down, I am oscillating. If I keep changing my mind, I am oscillating. In physics, we are more interested in bodies that move to and fro when left to their own. Examples include a swinging pendulum and a mass on a spring.
Consider a pendulum. This can be just a stone tied to a string. The other end of the string is tied to some support. If I lower the stone gently, it would just stay at rest directly below the support, with the string vertical. If I move the stone to one side and let go, it swings to and fro. Left to its own, it continues swinging for some time before it stops.
Lets look at this swinging in slow motion. When I first move the stone to one side, it also moves up slightly. This is because the string has a fixed length and it is now slanted. When I let go, the stone swings back to its rest position. This is because the force of gravity pulls it towards its lowest position.
When it reaches the rest position, it does not stop. It overshoots and moves to the opposite side. This is because it has gained momentum when it reaches the rest position. It cannot stop if there is no force to stop it.
After the stone overshoots the rest position, it also moves up slightly, because the string of fixed length becomes slanted again. The force of gravity comes into action, this time in the opposite direction to the velocity. This makes the stone slow down, stop, and move back towards the rest position.
The motion repeats, and we have oscillation.
In real life, this motion would not carry on for long. Air resistance and friction at the support both help to slow down the stone. The distance, or height, the stone travels decreases with every swing. Finally, it stops.
Usually, the stone could swing for many times before it stops. We can think of this as free oscillation. Of course, the stone is not entirely free. It is tied to the string, the force of gravity keeps pullling at it, and it cannot escape from the frictions. It is free in the sense that I am not holding it to make it oscillate, but that it oscillates on its own once I let go.
The example of a mass hanging from a spring is similar. If I pull the mass down and release it, it oscillates up and down.
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 19 March 2011.