Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 3 \cos 7 t$ inches after $t$ seconds. What are the frequency and period of the system?
A) Frequency $= 7$ cycles per sec, period $= \frac { 1 } { 7 } \mathrm { sec }$
B) Frequency $= \frac { 7 } { \pi }$ cycles per sec, period $= \frac { \pi } { 7 } \mathrm { sec }$
C) Frequency $= \frac { 7 } { 2 \pi }$ cycles per sec, period $= \frac { 2 \pi } { 7 } \mathrm { sec }$
D) Frequency $= \frac { \pi } { 7 }$ cycles per sec, period $= \frac { 7 } { \pi } \mathrm { sec }$

Question

Quizplus · Accepted Answer

The general form of a sinusoidal function is $s(t) = A \cos(Bt + C) + D$ or $s(t) = A \sin(Bt + C) + D$, where $B = \frac{2\pi}{T}$ and $T$ is the period. Here, $B = 7$, so the period $T = \frac{2\pi}{7}$ seconds. The frequency $f$ is the reciprocal of the period, $f = \frac{1}{T} = \frac{7}{2\pi}$ cycles per second.

Solve the Problem s(t)=−3cos⁡7ts ( t ) = - 3 \cos 7 ts(t)=−3cos7t

Solve the Problem $s ( t ) = - 3 \cos 7 t$