Как да изчислим Simple Harmonic Motion

Какво е 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.

Формула

x(t) = A × cos(ωt + φ); v = -Aω × sin(ωt + φ); a = -Aω² × cos(ωt + φ)

Ръководство стъпка по стъпка

1Enter amplitude A, angular frequency ω, initial phase φ
2Calculate position, velocity, and acceleration at time t
3Analyze period T = 2π/ω

Worked Examples

Вход

A = 0.5 m, ω = 2 rad/s, t = 0.5 s

Резултат

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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