Definition:Simple Harmonic Motion/Phase

Definition

Consider a physical system $S$ in a state of simple harmonic motion:

$x = A \map \sin {\omega t + \phi}$

The expression $\omega t + \phi$ is known as the phase of the motion.

Initial Phase

The parameter $\phi$ is known as the initial phase of the motion.

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

\(\ds x_1\)

\(=\)

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

\(\ds x_2\)

\(=\)

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

Out of Phase

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

In Phase

$S_1$ and $S_2$ are in phase if and only if $\alpha_1 = \alpha_2$.

Sources

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