Characteristics of Simple Harmonic Motion

Consider a ruler with one end fixed to a tabletop and the other end with a mass attached. When the ruler-mass system is pulled up from the free end and released, it executes simple harmonic motion. If the displacement is plotted with respect to time, this results in a sinusoidal waveform.

Since the oscillatory motion begins when the mass is displaced from the equilibrium position, the equation for displacement can be expressed as the amplitude, A, multiplied by the cosine function of the time-dependent angular frequency and initial phase.

Phase shift describes the difference between two similar waveforms in terms of the time interval and is measured in radians.

Recall that the first derivative of the displacement function with respect to time is velocity, and the second derivative is acceleration.

In simple harmonic motion, the velocity is a sine function that lags the displacement by phase pi by 2 and is maximum at the equilibrium, whereas the acceleration is a cosine function that lags by phase pi and is maximal at the positions of maximum displacement.