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1. SIMPLE PENDULUM AND
RESTORING FORCE

2. PERIODIC MOTION
The motion which
repeats itself after
fixed time intervals is
called periodic
motion
The best example of periodic motion are the pendulum clocks.

3. A SIMPLE PENDULUM
A string with a mass at
the end which is free to
swing is called a
pendulum.

4. TO AND FRO MOTION
The ball moves to
and fro. It rises to
extreme positions on
both sides and
reverses its motion
Oscillations gradually
die down

5. LENGTH OF THE PENDULUM
The length of the
string from the point
of suspension to the
mass is called the
length of the
pendulum.
It is denoted by L

6. MEAN POSITION OF THE PENDULUM
The central position of
the pendulum (the
starting position) is
called the mean
position of the
pendulum.
It is labeled here as B.

7. EXTREME POSITIONS OF THE
PENDULUM
A and C are the extreme positions of the pendulum.

8. OSCILLATION
The motion of the mass
from its extreme
position A to C and
back to A is called an
oscillation.

9. TIME TAKEN FOR ONE OSCILLATION
The time taken for one oscillation is very
short and therefore, difficult to measure
accurately.
To find the time taken, we find the time taken
for large number say 20 oscillations. This
time divided by 20 will give us time taken for
one oscillation.

10. PERIODIC TIME OF THE SIMPLE
PENDULUM
The time taken to complete one oscillation is
called the periodic time of the simple
pendulum.
It is sometimes also called its period and is
denoted by T.

11. RELATIONSHIP BETWEEN LENGTH AND
TIME PERIOD OF THE PENDULUM
The graph of the
relationship between
length and time period
of the pendulum is a
parabola.
Thus the relationship
can be expressed as
L=constant X T
2

12. VALUE OF CONSTANT
L= constant X T
2

constant=
2
T
L
By calculating the value of 2
T
L
2
T
L
for each value of the graph
between L and T
2
, the value of the
constant comes out to be 0.248

13. UNITS OF THE CONSTANT
The constant has the same
units as the acceleration that
is m/s
2
If we try to learn more about
the pendulum, we will find
that the constant is just the
acceleration g due to gravity
divided by

2
4

14. RELATIONSHIP BETWEEN T AND L
The equation is

g
L
2T
The Period of the pendulum T is related to the length L
by the relation