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Superposition of SHMs
Intermediate
Combine oscillations along the same line or at right angles.
Collinear SHMs of the same frequency add into one SHM with a new amplitude and phase. SHMs at right angles give ellipses or Lissajous figures.
x = 3 sin ωt + 4 cos ωt has amplitude 5.
Different frequencies give non-sinusoidal results.
In more detail
Two SHMs of the same direction and frequency add to a single SHM, whose amplitude depends on their phase difference. Adding perpendicular oscillations gives more complex patterns.
Real-world uses
- Engineers combine vibration sources to predict total vibration.
- Sound engineers combine waves to design speaker arrays.
- Sound waves from several instruments combine by superposition, which gives the complex tone of an orchestra.
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Frequently asked questions
When do two SHMs reinforce?
When they are in phase, giving the sum of their amplitudes.
When do they cancel?
When they are exactly out of phase and have equal amplitudes.
Can two perpendicular oscillations combine?
Yes. Perpendicular oscillations combine to give a path in the plane, which can be a line, circle or ellipse depending on phase.
Related topics in Oscillations & SHM
Coupled oscillators · Normal modes · Beats in oscillators · Lissajous figures · Anharmonic oscillation · Nonlinear oscillators