Objectives
The purposes of this experiment are: (1) to study the motion of a simple pendulum, (2) to
study simple harmonic motion, (3) to learn the definitions of period, frequency, and
amplitude, (4) to learn the relationships between the period, frequency, amplitude and
length of a simple pendulum and (5) to determine the acceleration due to gravity using
the theory, results, and analysis of this experiment.
Theory
A simple pendulum may be described ideally as a point mass suspended by a massless
string from some point about which it is allowed to swing back and forth in a place. A
simple pendulum can be approximated by a small metal sphere which has a small radius
and a large mass when compared relatively to the length and mass of the light string from
which it is suspended. If a pendulum is set in motion so that is swings back and forth, its
motion will be periodic. The time that it takes to make one complete oscillation is
defined as the period T. Another useful quantity used to describe periodic motion is the
frequency of oscillation. The frequency f of the oscillations is the number of oscillations
that occur per unit time and is the inverse of the period, f = 1/T. Similarly, the period is
the inverse of the frequency, T = l/f. The maximum distance that the mass is displaced
from its equilibrium position is defined as the amplitude of the oscillation.
When a simple pendulum is displaced from its equilibrium position, there will be a
restoring force that moves the pendulum back towards its equilibrium position. As the
motion of the pendulum carries it past the equilibrium position, the restoring force
changes its direction so that it is still directed towards the equilibrium position. If the
restoring force F
is opposite and directly proportional to the displacement x from the
