What is the Harmonic Motion Calculator?

The Harmonic Motion Calculator computes the displacement, velocity, and acceleration of a body undergoing simple harmonic motion (SHM) at a given time. It uses the standard SHM formulas: displacement x(t) = A·cos(ωt), velocity v(t) = -A·ω·sin(ωt), and acceleration a(t) = -A·ω²·cos(ωt), where A is amplitude, ω is angular frequency, and t is time. By entering these values, the calculator instantly provides all three key parameters, helping students, teachers, and physics enthusiasts analyze oscillatory motion and understand how the position, speed, and acceleration of a vibrating system change over time.

How to Use:

1. Enter Amplitude: Type the amplitude of oscillation in meters (m).
2. Enter Angular Frequency: Input the angular frequency in radians per second (rad/s).
3. Enter Time: Provide the time at which you want to calculate the motion in seconds (s).
4. Click “Calculate”: The calculator computes displacement, velocity, and acceleration at that instant.
5. Review the Result: The output shows all three quantities, making it easy to study wave motion, vibrations, or mechanical oscillations.