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 of the equation for simple harmonic motion is $d = A \cos(2\pi ft)$, where $f$ is the frequency. Comparing this to the given equation, $2\pi f = 18\pi$, solving for $f$ gives $f = \frac{18\pi}{2\pi} = 9$.

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