Fig. 14.1 shows some periodic motions. Suppose
process identically. If you draw a graph of its
look something like Fig. 14.1 (a). If a child climbs
look like that in Fig. 14.1 (b). When you play the
graph would look like the one in Fig. 14.1 (c).
Note that both the curved parts in Fig. 14.1 (c)
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. 14.1 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 call it oscillation (like,
the oscillation of a branch of a tree), while when
the frequency is high, we call it vibration (like,
the vibration of a string of a musical instrument).
Simple harmonic motion is the simplest form
of oscillatory motion. This motion arises when
the force on the oscillating body is directly
proportional to its displacement from the mean
position, which is also the equilibrium position.
Further, at any point in its oscillation, this force
is directed towards the mean position.
In practice, oscillating bodies eventually
come to rest at their equilibrium positions
because of the damping due to friction and other
dissipative causes. However, they can be forced
to remain oscillating by means of some external
periodic agency. We discuss the phenomena of
damped and forced oscillations later in the
chapter.
Any material medium can be pictured as a
collection of a large number of coupled
oscillators. The collective oscillations of the
constituents of a medium manifest themselves
as waves. Examples of waves include water
waves, seismic waves, electromagnetic waves.
We shall study the wave phenomenon in the next
chapter.
14.2.1 Period and frequency
We have seen that any motion that repeats itself
at regular intervals of time is called periodic
motion. The smallest interval of time after
which the motion is repeated is called its
period. Let us denote the period by the symbol
T. Its SI unit is second. For periodic motions,
(a)
(b)
(c)