Waves
SHM Acceleration
Acceleration proportional and opposite to displacement.
Variables
am/s²
Acceleration
Instantaneous acceleration
ωrad/s
Angular frequency
ω = 2πf
Allowed values: greater than 0
xm
Displacement
Position from equilibrium
Derivation
a = dv/dt = -Aω² cos(ωt + φ) = -ω²x.
Your notes
0/5000
Check value
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- ω = 2 rad/s (Angular frequency)
- x = 3 m (Displacement)
Result: a = -12 m/s²
Other waves formulas with the same quantities
- SHM Maximum Velocity (Simple Harmonic Motion) shares Angular frequency
- SHM Total Energy (Simple Harmonic Motion) shares Angular frequency
- Damped Oscillation (Simple Harmonic Motion) shares Displacement
- Angular Frequency (Wave Properties) shares Angular frequency
- Group Velocity (Wave Properties) shares Angular frequency
- Phase Velocity (Wave Properties) shares Angular frequency
Where this formula is listed
- Waves formulas, under Simple Harmonic Motion, alongside Spring Oscillation Period, Pendulum Period, Physical Pendulum Period, Torsional Oscillation Period and Quality Factor (Q Factor).
- In the waves list it comes after SHM Velocity and before SHM Maximum 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 Acceleration formula?
SHM Acceleration is written a = −ω²x. Acceleration proportional and opposite to displacement. It belongs to Waves, under Simple Harmonic Motion.
What are the units in a = −ω²x?
In SI units, a is acceleration, measured in m/s²; ω is angular frequency, measured in rad/s; x is displacement, measured in m.
How is the SHM Acceleration formula derived?
a = dv/dt = -Aω² cos(ωt + φ) = -ω²x. The result is a = −ω²x.