The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion
A) $\frac { 1 } { 3 \pi }$

B) $\frac { 1 } { 6 \pi }$

C) $6 \pi$
D) $3 \pi$
E) $2 \pi$

Question

The function $y = - 2 \cos \left( \frac { t } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the frequency of motion
A) $\frac { 1 } { 3 \pi }$

B) $\frac { 1 } { 6 \pi }$

C) $6 \pi$
D) $3 \pi$
E) $2 \pi$

Quizplus · Accepted Answer

The frequency of a cosine function $y = a \cos(bt)$ is given by $\frac{b}{2\pi}$. Here, $b = \frac{1}{3}$, so the frequency is $\frac{\frac{1}{3}}{2\pi} = \frac{1}{6\pi}$.

The Function y=−2cos⁡(t3)y = - 2 \cos \left( \frac { t } { 3 } \right)y=−2cos(3t​)

The Function $y = - 2 \cos \left( \frac { t } { 3 } \right)$