Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }$ inches after $\mathrm { t }$ seconds. What are the frequency and period of the system?
A) Frequency $= \frac { \pi } { 7 }$ cycles per sec, period $= \frac { 7 } { \pi } \mathrm { sec }$
B) Frequency $= \frac { 7 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 7 } \mathrm { sec }$
C) Frequency $= \frac { 7 } { \pi }$ cycles per sec, period $= \frac { \pi } { 7 } \mathrm { sec }$
D) Frequency $= 7$ cycles per sec, period $= \frac { 1 } { 7 } \mathrm { sec }$

Question

Quizplus · Accepted Answer

The frequency of a cosine function of the form $s(t) = A \cos(Bt)$ is given by $f = \frac{B}{2\pi}$ cycles per second, and the period is the reciprocal of the frequency, $T = \frac{1}{f} = \frac{2\pi}{B}$. For $s(t) = -2\cos(7t)$, $B = 7$, so the frequency is $f = \frac{7}{2\pi}$ cycles per second, and the period is $T = \frac{2\pi}{7}$ seconds.

Determine the Equation of the Graph s(t)=−2cos⁡7t\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }s(t)=−2cos7t

Determine the Equation of the Graph $\mathrm { s } ( \mathrm { t } ) = - 2 \cos 7 \mathrm { t }$