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How does the phase constant ϕ intervene in the equation of a sine wave?

How does the phase constant ϕ intervene in the equation of a sine wave?

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Answer #1

According to the equation of Sine wave. x = A sin ( ω t + ϕ )

describes the displacement motion of a passive linear harmonic oscillator without loss. In other words there is no input or driving function. Whatever motion the oscillator exhibits is solely due to its initial conditions. ϕ in this case provides a point of reference in space for the oscillations.

But for the driven oscillator, ϕ provides a more significant role in terms of how efficiently energy is transferred from the driver to to the oscillator (system). If the driving force is in perfect phase with the system and pointing in the right direction, maximum energy is transferred at the harmonic resonant frequency. Either side of this point either leads or lags, decreasing the efficiency of energy transfer.

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