Simple Harmonic Motion

For a system executing simple harmonic motion, the displacement, velocity, and acceleration are related through their phase differences:
- The displacement is given by: where is the amplitude, and is the angular frequency. - The velocity is the time derivative of displacement: The velocity leads the displacement by a phase of . - The acceleration is the time derivative of velocity: The acceleration lags the velocity by a phase of , and thus, lags the displacement by a phase of .
Thus, displacement lags both velocity and acceleration by the phases of and , respectively.