A simple pendulum consists of a string, cord, or wire that allows a suspended mass to swing back and forth. The categorization of "simple" comes from the fact that all of the mass of the pendulum is concentrated in its "bob" - or suspended mass.
As seen in this diagram, the length of the pendulum is measured from the pendulum's point of suspension to the center of mass of its bob. Its amplitude is the string's angular displacement from its vertical or its equilibrium position. If a pendulum is pulled to the right side and released to swing back and forth, its path traces our a sine curve as shown below.
The time required for one complete vibration, for example, from one crest to the next crest, is called the pendulum's period and is measured in seconds.
The formula to calculate this quantity is
This quantity at sea level is 9.81 m/sec2 and can be calculated as
G = 6.67 x 10-11 nt m2/kg2
Earth is the mass of the earth (6.02 x 1024 kg)
Earth is the average radius of the earth (6.4 x 106 meters)
Notice in the formula that the mass of a simple pendulum's bob does not affect the pendulum's period; it will however affect the tension
in the pendulum's string.
In this related lesson
, you will find a derivation
of this formula for the period of a simple pendulum that will help you understand the restrictions on its use. It will also explain to you why a simple pendulum is NOT a true representation of simple harmonic motion, SHM
. Take a few moments and use this physlet
to investigate how the period of a pendulum is impacted by its length and its initial displacement.
The frequency of a pendulum represents the number of vibrations per second. This quantity is measured in hertz (hz) and is the reciprocal of the pendulum's period.
Let's practice a few problems with these formulas.