7.3 Representing and Analyzing SHM

Displacement Function

In SHM, displacement from equilibrium varies sinusoidally with time. The displacement function can be modeled using either a sine or cosine function, depending on initial conditions.

Important Equation: ${x(t) = A \cos(\omega t + \phi)}$

${x(t)}$ = position at time t

${A}$ = amplitude (maximum displacement)

${\omega}$ = angular frequency

${\phi}$ = phase constant (determines starting position)

Amplitude represents the maximum distance from equilibrium, but it does not affect the period or frequency.