The motion of the body is said to be oscillatory or vibratory motion if it moves back and forth (to and fro) about a fixed position or point after a regular interval of time. Fixed point about which body oscillates is called mean position and equilibrium position. Every oscillatory motion is periodic but every periodic motion is not oscillatory. Some of the examples of oscillatory motion are: Vibration of wire of sitar and oscillation of the mass suspended from spring.
Examples of Oscillation
1. Simple Pendulum
If a heavy point mass is suspended by a weightless, inextensible and perfectly flexible string from a rigid support then this arrangement is called a simple pendulum.
Expression for time period:
For an angular momentum, sin θ, so that
F = -mgsin θ
= -( mg/l )y = -Ky
Because Y = lθ, thus the time period of the simple pendulum is: T=2π√L/g. This equation is valid only when the length of simple pendulum (l) is negligible as compared to radius of earth.
If a simple pendulum of density rho is made to oscillate in a liquid of density rho then its time period will increase as compare to that of air and is given by:
If the bob of a simple pendulum has positive charge q and the pendulum is placed in an uniform electric field E which is in vertical downward direction then time period decreases.
2. Compound Pendulum
Any rigid body which is free to oscillate in a vertical plane about a horizontal axis passing through a point, is define as compound pendulum
Different Types of Oscillations
Free, damped, forced resonant and coupled oscillations:
A. Free oscillation: The oscillation of a particle with fundamental frequency under the influence of restoring force are defined as free oscillations. The amplitude, frequency and energy of oscillations remain constant. The oscillator which keeps on oscillating with constant amplitude for infinite time is known as free oscillation.
B. Damped oscillations: The oscillation of a body whose amplitude goes on decreasing with time are defined as damped oscillations. In these oscillations the amplitude of oscillation decreases exponentially due to damping forces like frictional force, viscous force etc.
C. Forced oscillation: The oscillation in which the body oscillates under the influence of an external periodic force (driver) are known as forced oscillation. The driven body doesn't oscillate with its natural frequency rather it oscillates with frequency of the driver. The amplitude of the oscillator decreases due to damping force but on account of the energy gained from the external source (driver) it remains constant. The amplitude of forced vibration is determined by difference between the frequency of applied force and the natural frequency.
D. Resonance: When frequency of external force (driver) is equal to natural frequency of the oscillator (driven), then this state of driven and driven is known as state of resonance. In the state of resonance there occurs maximum transfer of energy from driven to driver. Hence the amplitude of motion becomes maximum. In the state of resonance frequency of the driver is known as the resonant frequency.
E. Coupled oscillation: A system of two or more oscillations linked together in such a way that there is mutual exchange of energy between them is called a coupled system. The oscillations of such a system are called coupled oscillations. The examples of coupled systems are as under:
Two masses attached to each other by three springs between two rigid supports. The middle spring can be viewed as a coupling between the driven system and driving system.
Two simple pendulums hanging from the same rigid support with their bobs attached to each other by a spring.