Find the frequency of the simple harmonic motion described by the function below. $$d = - 3 \cos ( 18 \pi t )$$
A) 9
B) $- \frac { 2 \pi } { 3 }$
C) $18 \pi$
D) $- \frac { 2 } { 3 }$
E) $- 3$

Question

Quizplus · Accepted Answer

The frequency of a simple harmonic motion described by $d = - 3 \cos ( 18 \pi t )$ is determined by the coefficient of $t$ inside the cosine function, which is $18\pi$. The general form for such a motion is $d = A \cos(\omega t + \phi)$, where $\omega = 2\pi f$, and $f$ is the frequency. Here, $\omega = 18\pi$, so $18\pi = 2\pi f$, leading to $f = 9$.

Find the Frequency of the Simple Harmonic Motion Described by the Function