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Oscillations and periodic motion
Position in SHM

12. Oscillations and periodic motion

Position in SHM

In 12. Oscillations and periodic motion

Formula

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

Tags

physics
physics formula
SHM
oscillations

Detail

Position in simple harmonic motion, of amplitude A and initial phase φ.

Explore the idea

Explore the idea

Variables

$A$ amplitude
$A$ initial phase.

Intuitive explanation

En MAS la posición oscila sinusoidalmente alrededor del equilibrio con amplitud $A$ y fase inicial $\phi$ .

Derivation

La solución de

\mathrm{d}^2x/\mathrm{d}t^2=-\omega^2x

es

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

.

Worked example

Con

A=0{,}10\,\mathrm{m}

,

\omega=4\,\mathrm{rad/s}

y

\phi=0

, a

t=\pi/4\,\mathrm{s}

se tiene

x\approx 0{,}071\,\mathrm{m}

.

Also known as

simple harmonic motion position
movimiento armónico simple

Last reviewed: 2026-09-14

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Related formulas

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Acceleration in SHM
$a=-\omega^2x$
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Velocity in SHM
$v=-A\omega\sin(\omega t+\phi)$
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