How to Calculate Simple Harmonic Motion
What is Simple Harmonic Motion?
Simple harmonic motion (SHM) describes oscillatory motion where acceleration is proportional to displacement and opposite in direction. Springs and pendulums exhibit SHM.
Formula
x(t) = A × cos(ωt + φ); v = -Aω × sin(ωt + φ); a = -Aω² × cos(ωt + φ)
Step-by-Step Guide
- 1Enter amplitude A, angular frequency ω, initial phase φ
- 2Calculate position, velocity, and acceleration at time t
- 3Analyze period T = 2π/ω
Worked Examples
Input
A = 0.5 m, ω = 2 rad/s, t = 0.5 s
Result
x ≈ 0.24 m, v ≈ -0.87 m/s
Oscillation position and velocity
Common Mistakes to Avoid
- ✕Confusing angular and regular frequency
- ✕Incorrect phase initial conditions
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