Page 49 - Physics - XI

The nearest approach to the ideal simple pendulum consists of a Rigid support
small metallic sphere (bob) suspended from a fi xed support by a Point of suspension
fi ne and inelastic silk or a cotton thread.

The oscillatory motion of a simple pendulum suspended from a
rigid support is shown in Fig. 7.3. If the bob of a simple pendulum
is displaced to one extreme position B and release, the bob returns Mean Extreme
position
to mean position A, goes to extreme left position C, returns to mean position
position A and again returns to its initial position B. This completes C A B
one oscillation. C A B
Amplitude
Time Period of Simple Pendulum
The time period T of a simple pendulum is given by the following

relation: Fig. 7.3: Motion of a simple pendulum

l and damped oscillations
T = 2π
g

where l is the length of the simple pendulum and g is the acceleration due to gravity.

Some useful defi nitions related with S.H.M.
1. Periodic motion: A motion which repeats itself after equal intervals of time is called periodic motion.

2. Oscillatory motion: The periodic motion in which a body moves to and fro about a fi xed point over
the same path is called oscillatory motion.

3. Simple harmonic motion (S.H.M.): An oscillatory motion which can be expressed in terms of a
single harmonic function (i.e. sine or cosine functions) is called S.H.M.
4. Displacement: The distance of vibrating particle from its mean position at any instant is called its
displacement.

5. Amplitude: The maximum displacement on either side of the mean position of a oscillating particle is
called its amplitude.

6. One complete oscillation: The motion of oscillating particle from one extreme position to second
extreme position and back to the fi rst extreme position constitutes one complete vibration or oscillation.
7. Time period: The time taken by the vibrating particle to complete one complete oscillation is called
its time period.

8. Frequency: Total number of complete oscillations made by the oscillating particle in one second is
called frequency.

9. Length of simple pendulum: The distance between the point of the suspension and the centre of the
bob is called length of the simple pendulum.
10. Second's pendulum: A simple pendulum whose time period is two second is called second's pendulum.

Its length is about 99.3 cm (approximately one metre).

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