Waves
SHM Displacement
Position as function of time in SHM.
Variables
xm
Displacement
Position from equilibrium
Am
Amplitude
Maximum displacement
ωrad/s
Angular frequency
ω = 2πf
ts
Time
Time
φrad
Phase constant
Initial phase
Derivation
Solution to d²x/dt² = -ω²x.
Your notes
0/5000
Other waves formulas with the same quantities
- SHM Maximum Velocity (Simple Harmonic Motion) shares Amplitude, Angular frequency
- SHM Total Energy (Simple Harmonic Motion) shares Amplitude, Angular frequency
- Damped Oscillation (Simple Harmonic Motion) shares Displacement, Time
- Angular Frequency (Wave Properties) shares Angular frequency
- Intensity-Amplitude Relation (Wave Properties) shares Amplitude
- Group Velocity (Wave Properties) shares Angular frequency
Where this formula is listed
- Waves formulas, under Simple Harmonic Motion, alongside Pendulum Period, Physical Pendulum Period, Torsional Oscillation Period, Quality Factor (Q Factor) and Resonance Amplitude.
- In the waves list it comes before SHM Velocity.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the SHM Displacement formula?
SHM Displacement is written x = A cos(ωt + φ). Position as function of time in SHM. It belongs to Waves, under Simple Harmonic Motion.
What are the units in x = A cos(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 = A cos(ωt + φ).