This document describes an experiment to determine the effective length of a simple pendulum for a given time period using a graph. The experiment involves suspending a bob from a string or thread of varying lengths and measuring the time period for 20 oscillations using a stopwatch. An observation table is created to record the length, time period, and time period squared for each trial. A graph is then plotted of length versus time period squared, which produces a straight line. The graph is used to determine the effective length of the pendulum for a time period of 2 seconds. The experimental length is found to be 100 cm with less than 1% error from the actual length.

1. To Study the
Motion of the
Pendulum
Vansh Patil
11th C
S11C36

2. Index
• Objectives
• Apparatus
• Theory
• Procedure
• Observation Table
• Calculation
• Graph
• Result
• Precautions

3. Objectives
• To find the effective length of the simple pendulum
for a given time period using the graph.

4. Apparatus
• A clamp with stand
• A split cork
• A Cotton Thread (about 2
meters long)
• A bob
• Vernier caliper
• Stop /watch
• Meter scale.

5. Theory
• An ideal simple pendulum consists of a heavy point mass (called bob)
tied to one end of a perfectly inextensible, flexible and weightless
string. In practice, we make it by tying a metallic spherical bob to a fine
cotton stitching thread.
• Length of a Simple Pendulum
The distance between the point of suspension of the pendulum and its
Centre of Gravity (C.G.), which is the C.G. of the bob, is called the length
of the simple pendulum. It is represented using the alphabet ( l ).
• Time Period of a Simple Pendulum
Time period is the time taken by the bob of the simple pendulum to
make one complete oscillation. It is represented by the letter T.
• Finding the acceleration due to gravity
The time period of a simple pendulum depends on the length of the
pendulum (l) and the acceleration due to gravity (g).

6. Procedure
• Cut a piece of a string or dental
floss so that it is about 1 m
long. Attach a small object of
high density to the end of the
string (for example, a metal nut
or a car key). Starting at an
angle of less than 10º, allow
the pendulum to swing and
measure the pendulum’s
period for 10 oscillations using
a stopwatch. Calculate g.

7. Observation
Table

8. Calculations
• (a) With the table
• For each length, write mean time for 20 vibrations
• Write mean values of t in column (3) of above table.
• For each length, find time period T =t/20 s and write
its value in column 4 and write value of T2 in
column 5 of the above table.
• l-T2 graph. Plot a graph between l (column, 2b) and
T2 (column 5) by taking Z along X- axis and T2
along Y-axis. The graph comes to be a straight line.

9. Graph
From this graph, for T2 = 4, l comes to
be 100 cm.
Hence for seconds pendulum (T = 2 s)
length comes to be 100 cm.

10. Result
• Experimental length 100 cm Actual
length = 99.4 cm Error = 0.6 cm
• Percentage error = 0.6/99.4 x 100 =
0.6%
• This error is within the limit of the
experimental error.

11. Precautions
• Thread should be strong, weightless and in extensible.
• Point of suspension should be fixed in a rigid support.
• Lower faces of split cork should be in same level.
• Splitting should be perpendicular to the plane of vibration of the
pendulum.
• Amplitude should be small to have sin 0 = 0. [when 0 < 18°]
• The bob should move along a straight line.
• The bob should not spin during vibration.
• Place of experiment should be free from disturbances of building
vibrations or air current.
• Laboratory fan should be switched off.