COLLEGE PHYSICS LABORATORY EXPERIMENT
GRAVITATIONAL ACCELERATION I: SIMPLE PENDULUM
OBJECTIVES
• Verify that the period of oscillation of a simple pendulum is independent of its mass.
• Measure the near-Earth gravitational acceleration g.
THEORY
A pendulum is composed of an object of mass m (called a bob) attached to a fixed point
of support with the help of a massless string of length . When the pendulum is displaced
by an angle θ (as shown in the Figure below) and let go, the pendulum executes periodic
motion in the presence of the gravitational acceleration g.
It is easily shown (by dimensional analysis) that the period of oscillation T is proportional to (/g)1/2 for small angular displacements (< 15o ) and is independent of the mass
m of the bob – a simple pendulum is a pendulum whose period is independent of the initial
angular displacement.
More careful analysis (to be carried out later in the course) shows that the period of a
simple pendulum is given as
T
=
,
2π
g
where the dimensionless factor 2π is needed on mathematical grounds.
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MATERIAL & PROCEDURE
• Material: string, pendulum bob of varying mass, electronic scale, stopwatch,
and meter stick.
• Procedure I
◦ Measure mass m of a pendulum bob.
◦ Attach pendulum bob to a piece of string and measure length (taking into
account the size of the bob).
◦ Measure time interval ∆t associated with 10 oscillations of the simple pendulum
and calculate its period T = ∆t/10.
◦ Repeat 4-5 times by changing the mass m of the pendulum bob without changing
the length .
• Procedure II
◦ Measure mass m of a pendulum bob.
◦ Attach pendulum bob to a piece of string and measure length (taking into
account the size of the bob).
◦ Measure time interval ∆t associated with 10 oscillations of the simple pendulum
and calculate its period T = ∆t/10.
◦ Repeat at least 7-8 times by changing the length of the pendulum without changing
the mass m of the pendulum bob.
DATA ANALYSIS
• Perform the data analysis to determine the relationship between period T of the simple
pendulum and its mass m.
• Calculate the experimental value for gexp , its percent uncertainty, and its percent error
compared to gth .
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