Summary Points to ponder Exercises . PERIODIC AND OSCILLATORY MOTIONS Fig. . shows some periodic motions.
Suppose an insect climbs up a ramp and falls down, it comes back to the initial point and repeats the process identically. If you draw a graph of its height above the ground versus time, it would look something like Fig. . (a).
If a child climbs up a step, comes down, and repeats the process identically, its height above the ground would look like that in Fig. . (b). When you play the game of bouncing a ball off the ground, between your palm and the ground, its height versus time graph would look like the one in Fig.
. (c). Note that both the curved parts in Fig. .
(c) are sections of a parabola given by the Newton’s equation of motion (see section . ), + gt h = ut for downward motion, and – gt h = ut for upward motion, with different values of u in each case. These are examples of periodic motion. Thus, a motion that repeats itself at regular intervals of time is called periodic motion.
Fig. . Examples of periodic motion. The period T is shown in each case.
Very often, the body undergoing periodic motion has an equilibrium position somewhere inside its path. When the body is at this position no net external force acts on it. Therefore, if it is left there at rest, it remains there forever. If the body is given a small displacement from the position, a force comes into play which tries to bring the body back to the equilibrium point, giving rise to oscillations or vibrations .
For example, a ball placed in a bowl will be in equilibrium at the bottom. If displaced a little from the point, it will perform oscillations in the bowl. Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. Circular motion is a periodic motion, but it is not oscillatory.
There is no significant difference between oscillations and vibrations. It seems that when the frequency is small, we