Chapter 23 : Simple Harmonic Motion 471
It will be interesting to know that when the point P moves round the circumference of the
circle from x to y, N moves from O to y ; when P moves from y to x', N moves from y to O.
Similarly, when P moves from x' to y', N moves from O to y', and finally when P moves from y' to
x, N moves from y' to O. Hence, as P completes one revolution, the point N completes one vibration
about the point O. This to and fro motion of N is known as Simple harmonic motion, briefly
written as S.H.M.
23.2.IMPORTANT TERMS
The following terms, which will be frequently used in
this chapter, should be clearly understood at this stage :
- Amplitude. It is the maximum displacement of a
body, from its mean position. In Fig. 23.1, Oy and
Oy' is the amplitude of the particle N. The
amplitude is always equal to the radius of the
circle. - Oscillation. It is one complete vibration of a body.
In Fig. 23.1, when the body moves from y to y'
and then back to y (or in other words from O to y,
y to y' and then y' to O), it is said to have completed
one oscillation. - Beat. It is half of the oscillation. In Fig. 23.1, when
the body moves from y to y' or y' to y (or in other words O to y' and then y' to O), it is said
to have completed one beat. - Periodic time. It is the time taken by a particle for one complete oscillation. Mathematically,
periodic time,
2
T
π
=
ω
where ω = Angular velocity of the particle in rad/s.
It is thus obvious, that the periodic time of a S.H.M. is independent of its amplitude.- Frequency. It is the number of cycles per second and is equal to
1
T
where T is the periodic
time. Frequency is generally denoted by the letter ‘n’. The unit of frequency is hertz
(briefly written Hz) which means frequency of one cycle per second.23.3.GENERAL CONDITIONS OF SIMPLE HARMONIC MOTION
In general, a body is said to move or vibrate, with simple harmonic motion, if it satisfies the
following two conditions :
- Its acceleration is always directed towards the centre, known as the point of reference or
mean position. - Its acceleration is proportional to the distance from that point.
Fig. 23.1. S.H.M.