How to use the simple harmonic motion calculator
Find position, velocity and acceleration of an oscillator at a given time. Enter amplitude, frequency, time in the fields above; the displacement, velocity, acceleration, max speed are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- A — Amplitude (m)
- f — Frequency (Hz)
- t — Time (s)
Worked example
With amplitude = 0.1 m, frequency = 2 Hz, time = 0.1 s, the calculator gives displacement ≈ 0.0309017 m; velocity ≈ -1.195133 m/s; acceleration ≈ -4.879801 m/s²; max speed ≈ 1.256637 m/s.
Frequently asked questions
What is the formula for the simple harmonic motion calculation?
Displacement (m) = A × cos(2 × π × f × t). Velocity (m/s) = -A × 2 × π × f × sin(2 × π × f × t). Acceleration (m/s²) = -A × (2 × π × f)^2 × cos(2 × π × f × t). Max speed (m/s) = A × 2 × π × f. Here A is amplitude (m), f is frequency (Hz), t is time (s).
What inputs do I need for the simple harmonic motion calculator?
You need amplitude in m, frequency in Hz, time in s. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.