Course description

A particle may be simultaneously acted upon by more than one simple harmonic vibrations acting either along the same straight line or at right angles to each other. The resultant displacement, velocity, acceleration, etc., of the particle is given by the vector sum of the corresponding quantities due to the individual waves.

Combination of two simple harmonic vibrations of same frequency but different phase and amplitude:  Let a particle in a medium be simultaneously acted upon by two simple harmonic vibrations of same frequency but different phase and amplitude given by the following equations,

Combination of two simple harmonic vibrations at right angles to each other having equal frequencies but differing in phases and amplitudes:

Let us consider two simple harmonic motions of the same frequency (i.e., same time period) but of amplitude a and b and having their vibrations mutually perpendicular to one another. If φ is the phase difference between the two vibrations, then their equations can be written as

Lissajous’ figures: The combination of two simple harmonic vibrations in mutually perpendicular directions gives rise to an elliptical path. The shape of the curve will depend upon the phase difference between the two vibrations and also on the ratio of the frequencies of the component vibrations. These figures or curves (like Figs 6 a-d) were first produced optically by Lissajous by reflecting a beam of light from two mirrors, in turn attached to two forks vibrating at right angles to one another. These figures are known as Lissajous’ figures.

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