SIMPLE PENDULUM AND RESTORING FORCE. PERIODIC MOTION The motion which repeats itself after fixed...

SIMPLE PENDULUM AND RESTORING FORCE

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.

A SIMPLE PENDULUM

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

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

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

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.

EXTREME POSITIONS OF THE PENDULUM

A and C are the extreme positions of the pendulum.

OSCILLATION

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

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.

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.

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 T2

VALUE OF CONSTANT

L= constant X T2

constant= 2T

L

By calculating the value of 2T

L

2T

L

for each value of the graph between L and T2, the value of the constant comes out to be 0.248

UNITS OF THE CONSTANT

The constant has the same units as the acceleration that

is m/s2

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

24

RELATIONSHIP BETWEEN T AND L

The equation is

gL

2T

The Period of the pendulum T is related to the length L by the relation