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Phasor representation
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Project a rotating vector to get SHM.
Represent x = A cos(ωt + φ) as a rotating arrow of length A at angle ωt + φ. Adding oscillations of the same frequency means adding arrows.
Two SHMs of amplitude 3 and 4 in quadrature give 5.
Only the projection is physical.
In more detail
A phasor is a rotating vector whose projection onto an axis gives a sinusoidal quantity. Phasors turn oscillations into vector additions, which simplifies calculations.
Real-world uses
- Electrical engineers analyse AC circuits using phasors.
- Adding two sinusoids of the same frequency is done by adding their phasors.
- Electrical engineers use rotating phasor diagrams to add alternating voltages, which is much faster than solving sinusoids directly.
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Frequently asked questions
How is a phasor drawn?
As an arrow whose length is the amplitude and whose angle is the phase.
Why do they rotate?
The angle increases at the angular frequency, so the projection oscillates.
What does a phasor represent?
A vector rotating at the angular frequency, whose projection on an axis gives the sinusoidal quantity.
Related topics in Oscillations & SHM
Angular frequency · Phase and phase constant · Phase difference · Mass–spring system · Vertical spring · Springs in series/parallel oscillations