Another mechanical device that operates in an oscillating motion is the simple pendulum.
It consists of a point mass 'm' hung from fixed support by a light inextensible string of length L.
The motion happens in a vertical plane and is caused by gravity.
The figure shows the illustration of a simple pendulum:
All the forces acting on the mass are given below. Assumptions are that the tension in the string is constant throughout the length of the string.
Solution:
Since the period where g is the acceleration due to gravity, the laws of the pendulum can be concluded as follows:
If the amplitude is small enough, the period of the simple pendulum is independent of it. The law of isochronism refers to this feature.
The basic pendulum's period is directly proportional to the square root of its length. The law of length refers to this feature.
A simple pendulum's period is inversely proportional to the square root of the acceleration due to gravity at that location. This feature is known as the law of gravitational acceleration.
The period of oscillation of a pendulum at a point is independent of the mass and material of the bob if the effective length of the pendulum is constant. The law of mass refers to this characteristic.
These are the empirical laws of a simple pendulum.
