Simple harmonic motion calculator
Enter the amplitude, frequency, phase angle and time, and get the displacement u(t), the velocity and the acceleration, together with the angular frequency and the period.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The formulas
For an oscillation u(t) = A · sin(2πf·t + φ):
- angular frequency ω = 2πf
- period T = 1/f
- velocity v(t) = Aω · cos(ωt + φ)
- acceleration a(t) = −Aω² · sin(ωt + φ)
The acceleration always points back towards the middle and is largest at the extremes, where the velocity is zero.
Examples
A mass on a spring, a pendulum with small swings, a tuning fork and alternating current all follow this motion. Enter the frequency in hertz and the time in seconds; the phase angle can be in radians or degrees.
Frequently asked questions
Is the simple harmonic motion free?
Yes. The simple harmonic motion is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.