For the simple harmonic motion described by the trigonometric function, find the frequency per second.
$d = 9 \cos \frac { 8 \pi } { 5 } t$
A) $\frac { 4 } { 5 }$
B) $\frac { 8 \pi } { 5 }$
C) $\frac { 5 } { 4 }$
D) $\frac { 5 \pi } { 8 }$
E) $\frac { 5 } { 8 }$

Question

For the simple harmonic motion described by the trigonometric function, find the frequency per second.   
$d = 9 \cos \frac { 8 \pi } { 5 } t$  
A) $\frac { 4 } { 5 }$
B) $\frac { 8 \pi } { 5 }$
C) $\frac { 5 } { 4 }$
D) $\frac { 5 \pi } { 8 }$
E) $\frac { 5 } { 8 }$

Quizplus · Accepted Answer

The frequency of a trigonometric function in simple harmonic motion is given by the coefficient of $t$ in the argument of the cosine function, divided by $2\pi$. Here, the coefficient of $t$ is $\frac{8\pi}{5}$, so the frequency $f = \frac{\frac{8\pi}{5}}{2\pi} = \frac{4}{5}$ Hz.

For the Simple Harmonic Motion Described by the Trigonometric Function d=9cos⁡8π5td = 9 \cos \frac { 8 \pi } { 5 } td=9cos58π​t

For the Simple Harmonic Motion Described by the Trigonometric Function $d = 9 \cos \frac { 8 \pi } { 5 } t$