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Harmonic oscillation

A harmonic oscillator moves back and forth around an equilibrium position with a displacement that follows a cosine function. The amplitude is the largest displacement, the angular frequency tells you how fast the phase changes, and the period is the time for one full oscillation.

x(t) = A\cos(\omega t + \varphi)

displacement as a function of time

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

relation between angular frequency, frequency and period

Symbols

$A$	amplitude	m
$\omega$	angular frequency	rad/s
$f$	frequency	Hz
$T$	period	s

Example

An oscillation has $f = 4.0$ Hz. The angular frequency is $\omega = 2\pi\cdot 4.0 \approx 25.1$ rad/s, and the period is $T = 1/4.0 = 0.25$ s.

Do not mix up

\omega

(rad/s) and

f

(Hz) – they differ by a factor of

2\pi

Practise oscillations and waves for free →

Mass–spring and pendulum →

Part of Physics: Oscillations and waves.