Simple Harmonic Motion

About this calculator

The Simple Harmonic Motion Calculator finds the instantaneous position, velocity, and acceleration of an oscillator described by x(t) = A·cos(ωt + φ). Enter the amplitude, angular frequency, phase angle, and time to get the displacement x(t) = A·cos(ωt + φ), velocity v(t) = −Aω·sin(ωt + φ), and acceleration a(t) = −ω²·x(t), along with the period, frequency, maximum speed, and maximum acceleration. Every value is computed with 30-digit precision and the curve shows where the oscillator is at the chosen moment. Useful for physics homework, springs, pendulums in the small-angle limit, and any oscillating system.

How to use the Simple Harmonic Motion calculator

1. Enter the quantities you know, using the units shown on each field.
2. Read the computed results — they update instantly as you type.
3. Use the visual explanation to see how the quantities relate.
4. Copy the page URL to share the exact calculation.

Common examples

• A = 1 m, ω = 1 rad/s, φ = 0°, t = 0 s → x = 1 m, v = 0 m/s, a = −1 m/s²
• A = 2 m, ω = 3 rad/s, φ = 0°, t = 0 s → x = 2 m, v = 0 m/s, a = −18 m/s²
• A = 1 m, ω = 2 rad/s, φ = 90°, t = 0 s → x = 0 m, v = −2 m/s, a = 0 m/s²
• ω = 2π rad/s → period T = 1 s, frequency f = 1 Hz
• A = 0.5 m, ω = 4 rad/s → max speed 2 m/s, max acceleration 8 m/s²