Introduction
Oscillatory motion, or periodic motion, is the most common type of motion. Heartbeat of animals, the seasons of the year, the swinging of the pendulum of a clock and the vibrations of atoms in solids are periodic in nature.
Simple Harmonic Motion
In the preceding sections, the motion of a body when acted upon by a constant force was considered. The motion is one of constant acceleration.
Characteristics of SHM
The body returns to a given point in the path with the same velocity after regular intervals of time.
The Circle of Reference
The maximum displacement of the particle executing SHM from the equilibrium position is known as the amplitude. It will be equal to the radius of the circle of reference. Therefore, the total range of motion is 2A.
Expression for Displacement in SHM
The foot of the perpendicular drawn from the body onto any diameter executes SHM.
Expression for Acceleration in SHM
A body moving along a circular path is acted upon the centripetal acceleration.
Expression for Period in SHM
The force constant of the spring (or any other agency) which supplies the restoring force.
Energy in SHM
To cause a displacement of a body controlled by elastic forces, work has to be done. For example, work has to be done in stretching a spring against the elastic forces. This work will be stored in the body as potential energy. When the deforming force is released, this potential energy manifests in the form of kinetic energy which makes the body to move. Thus, a body in SHM, has both potential energy and kinetic energy.
Phase Constant in SHM
Consider the case when a body moving in a circular path is not at Qo but at Q when t = 0.
Period of a Simple Pendulum
A simple pendulum is an arrangement in which a point mass is suspended by an inextensible weightless string in a uniform gravitational field. This is an ideal system which cannot be realized in practice. However, a pendulum consisting of a small but relatively heavy bob on one end of a very light string can be considered as a simple pendulum.
Frictional Effects
An oscillator, in actual practice, almost always lies in a resisting medium, like air, oil etc., where part of its energy is dissipated in overcoming the opposing frictional or viscous forces and its amplitude, therefore, goes on decreasing progressively. Such forces, which are non-conservative in nature, have thus a damping, resistive or dissipative forces.
Two Body Harmonic Oscillator
Some objects have a wide range of lengths in the universe.
