Definition:Simple Harmonic Motion/Out of Phase

Definition

Let $S_1$ and $S_2$ be physical systems in a state of simple harmonic motion described respectively by the equations:

\(\ds x_1\)

\(=\)

\(\ds a_1 \map \cos {\omega t + \alpha_1}\)

\(\ds x_2\)

\(=\)

\(\ds a_2 \map \cos {\omega t + \alpha_2}\)

$S_1$ and $S_2$ are out of phase if and only if $\alpha_1 \ne \alpha_2$.

Phase Difference

The phase difference of $S_1$ and $S_2$ is defined as $\size {\alpha_1 - \alpha_2}$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): harmonic motion
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): harmonic motion