# Investigatory Project on Simple Pendulum

Physics Investigatory Project on Simple Pendulum

Aim: To study about the factors upon which the period of oscillation of a simple pendulum depends.

Apparatus: Simple Pendulum, Bob of different masses, Stop watch, Meter Scale etc.

A simple pendulum having a metallic bob hanged by a light inextensible string. The upper portion of the string is passed all the way through a split cork which is clamped strongly to a stand. The length of the pendulum is the distance between the point of suspension to the centre of gravity of the bob.

Theory:

The period of oscillation of a simple pendulum is given by,

T = 2π(l/g)

Where, l = length of the pendulum

g = acceleration due to gravity at the place

Procedure:

1. To study how the length of the pendulum depends

The pendulum is suspended from a fixed point. The length of the pendulum is adjusted to be about 50 cm. The time for 20 oscillations is determined and the period of oscillation is calculated. The experiment is repeated for different lengths and in each case the period is calculated.

2. To study how the amplitude of the pendulum depends

The experiment is repeated by keeping the length as a constant for different amplitudes (we prefer small amplitude). For this the edge of the table parallel to the plane of oscillation of the pendulum is marked at different distances from the mean position so as to represent different amplitudes. The period of oscillation is found for different amplitude of oscillations.

3. To study how the mass of the bob depends

The experiment is repeated by using bobs of different masses keeping the length of the pendulum and amplitude constant. The period of oscillation is determined in each case.

Observations and Calculations

i. To study how the length of the pendulum depends

Amplitude of oscillation = ...........cm

Mass of the bob = ........g

 Trial No: Length of the pendulum Time for 20 oscillations Period, T = t/20 1 2 Mean(t) cm s s s s 1 2 3 4 5 6

ii. To study how the amplitude of the pendulum depends

Length of the pendulum = .......cm

Mass of the bob = .......g

 Trial No: Length of the pendulum Time for 20 oscillations Period, T = t/20 1 2 Mean(t) cm s s s s 1 2 3 4 5 6 4 8 12 16 18

iii. To study how the mass of the bob depends

Length of the pendulum = .......cm

Amplitude of oscillation = .......cm

 Trial No: Mass of the bob Time for 20 oscillations Period, T = t/20 1 2 Mean(t) g s s s s 1 2 3 4 5 6 4 8 12 16 18

Report:

It is found that the period of oscillation of a simple pendulum at a place,

i. depends on the length of the pendulum

ii. independent of the amplitude of oscillation

iii. independent of the mass of the bob