Definition:Simple Harmonic Motion/Period

Definition

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

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

The period $T$ of the motion of $S$ is the time required for one complete cycle:

$T = \dfrac {2 \pi} \omega$

Also see

• Sine and Cosine are Periodic on Reals

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.20$: Vibrations in Mechanical Systems
• 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
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): angular frequency
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): angular frequency