SIMPLE PENDULUM AND RESTORING FORCE

PERIODIC MOTION

The motion whichrepeats itself after fixedtime intervals is calledperiodic motion

The best example of periodic motion are the pendulum clocks.

A SIMPLE PENDULUM

A string with a mass at theend which is free to swing iscalled a pendulum.

TO AND FRO MOTION

The ball moves to and fro. It rises to extremepositions on both sides and reverses its motion

Oscillations gradually die down

LENGTH OF THE PENDULUM

The length of thestring from the pointof suspension to themass is called thelength of thependulum.

It is denoted by L

MEAN POSITION OF THE PENDULUM

The central position ofthe pendulum (thestarting position) is calledthe mean position of thependulum.

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 massfrom its extreme positionA to C and back to A iscalled an oscillation.

TIME TAKEN FOR ONE OSCILLATION

The time taken for one oscillation is veryshort and therefore, difficult to measureaccurately.

To find the time taken, we find the timetaken for large number say 20 oscillations.This time divided by 20 will give us timetaken for one oscillation.

PERIODIC TIME OF THE SIMPLE PENDULUM

The time taken to complete one oscillation is calledthe periodic time of the simple pendulum.

It is sometimes also called its period and is denotedby T.

RELATIONSHIP BETWEEN LENGTH AND TIME PERIOD OF THE PENDULUM

The graph of therelationship betweenlength and time periodof the pendulum is aparabola.

Thus the relationshipcan be expressed as

L=constant X T2

VALUE OF CONSTANT

L= constant X T2

constant= 2TL

2T

LBy calculating the value of

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