Question

which equation can be used to model simple harmonic motion?
a. $d = a\cos(\omega t)$
b. $d = \cos(a\omega t)$
c. $d = a\sin(\omega t) + k$
d. $d = a\cos\omega(t + k)$

Explanation:

Simple harmonic motion is modeled by sinusoidal functions where:

• $a$ = amplitude (scales the oscillation range),
• $\omega$ = angular frequency (controls oscillation rate),
• The base form is either cosine or sine with the argument $\omega t$ (for motion starting at maximum displacement at $t=0$, cosine is used).
• Option B lacks an amplitude scale factor outside the trigonometric function.
• Option C adds a vertical shift $k$, which is for shifted harmonic motion, not the basic model.
• Option D includes a phase shift inside the function, which is a modified form, not the standard base model for simple harmonic motion.

Answer:

A. $d = a\cos(\omega t)$