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Waves
Waves

SHM Displacement

x=Acos⁡(ωt+ϕ)x = A\cos(\omega t + \phi)

Position as function of time in SHM.

Variables

x
Displacement
Position from equilibrium
m
A
Amplitude
Maximum displacement
m
ω
Angular frequency
ω = 2πf
rad/s
t
Time
Time
s
φ
Phase constant
Initial phase
rad

Derivation

Solution to d²x/dt² = -ω²x.

Your notes

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Common questions

What is the SHM Displacement formula?

SHM Displacement is written x = Acos(ωt + φ). Position as function of time in SHM. It belongs to Waves, under Simple Harmonic Motion.

What are the units in x = Acos(ωt + φ)?

In SI units, x is displacement, measured in m; A is amplitude, measured in m; ω is angular frequency, measured in rad/s; t is time, measured in s; φ is phase constant, measured in rad.

How is the SHM Displacement formula derived?

Solution to d²x/dt² = -ω²x. The result is x = Acos(ωt + φ).