Physics

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Simple Harmonic Motion Calculator.

Evaluate position, velocity, and acceleration for sinusoidal simple harmonic motion.

On-device calculationNo signup
01

Set your values

Results update as you type.

Angular frequency: 6.283185 rad/s

Angular frequency

0.000000rad/s
Position: 0 m

Position

0.000000m
Velocity: -0.628319 m/s

Velocity

0.000000m/s
Acceleration: -0 m/s²

Acceleration

0.000000m/s²

Results update automatically as you type.

Use Cases

Physics homework and exam prep

Quickly verify your manual calculations for position, velocity, and acceleration in SHM problems. Enter the given parameters and compare your answers.

Example: Check the velocity of a 0.5 m amplitude oscillator at 2 Hz and phase 0.3 rad after 0.1 s.

Engineering design of oscillating systems

Estimate the kinematic behavior of mechanical components that undergo sinusoidal motion, such as vibration isolators or cam followers, to ensure they operate within safe limits.

Example: Determine the maximum acceleration of a vibrating platform with amplitude 0.02 m and frequency 50 Hz.

Frequently Asked Questions

What does this simple harmonic motion calculator do?
It computes the position, velocity, and acceleration of an object undergoing sinusoidal simple harmonic motion. You input amplitude (m), frequency (Hz), phase (rad), and time (s), and it outputs the three kinematic quantities at that instant.
What units should I use for the inputs?
Use meters for amplitude, hertz for frequency, radians for phase, and seconds for time. The calculator will then output position in meters, velocity in meters per second, and acceleration in meters per second squared.
Can I use this calculator for any type of simple harmonic motion?
Yes, as long as the motion is sinusoidal. This includes mass-spring systems, pendulums (for small angles), and other oscillators. Just ensure you know the amplitude, frequency, and phase at the time of interest.

Tips & Common Mistakes

Tips

  • Ensure the frequency is in hertz (cycles per second) and phase is in radians, not degrees. If your phase is in degrees, convert to radians first.
  • Remember that the calculator gives instantaneous values at the specified time. For a full cycle, you would need to evaluate at multiple times.
  • Double-check your amplitude: it should be the maximum displacement from equilibrium, not the peak-to-peak distance.
  • Use consistent units. If you mix units (e.g., cm for amplitude), convert to meters before entering.

Common Mistakes to Avoid

  • Using degrees for phase instead of radians. The calculator expects radians, so convert degrees to radians (multiply by π/180).
  • Confusing frequency with angular frequency. The calculator uses frequency in Hz, not angular frequency (rad/s). If you have angular frequency, divide by 2π to get Hz.
  • Entering peak-to-peak amplitude instead of the amplitude. The amplitude is half the peak-to-peak distance.

Last updated: August 13, 2026