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

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 $\frac{2\pi}{B}$ is the period and $B$ is related to the frequency by $f = \frac{B}{2\pi}$. For $s(t) = -2\cos(3t)$, $B = 3$, so the frequency is $f = \frac{3}{2\pi}$ cycles per second and the period is $T = \frac{2\pi}{3}$ seconds.

Solve the Problem s(t)=−2cos⁡3s ( t ) = - 2 \cos 3s(t)=−2cos3

Solve the Problem $s ( t ) = - 2 \cos 3$