Simple Harmonic Motion & Phase

This applet shows a number of particles in Simple Harmonic Motion. All the particles have the same amplitude and frequency but are at different positions at any given moment. Phase expresses this difference. Each of the particles in motion can be associated with a particle on the circle. Phase is then the angular position of the particle on the circle. Phase increases continuously with time, going up by 2π radians for every oscillation. Since all the particles shown in the applet have the same frequency, the phase increases at the same rate for all of them and so the phase difference between them does not change with time.

Phase is one variable which can be related to all other variables easily (position, velocity, and acceleration). This means that knowing the constants of a SHM and the phase would be enough to completely define it.

When adding two or more simple harmonic motions, phase is a very important term. Imagine two SHMs of equal amplitude and frequency. If their phase difference is m*π radians (m: odd integer) the oscillations cancel each other (destructive interference), while if the phase difference is n*π (n: even integer or 0) they add up (constructive interference).

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