Solve the problem.
-A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.
A) $s ( t ) = - 4 \cos 10 t$
B) $s ( t ) = 4 \cos 10 \mathrm { t }$
C) $s ( t ) = 4 \pi \cos 5 t$
D) $s ( t ) = - 4 \cos \frac { 5 } { \pi } t$

Question

Quizplus · Accepted Answer

The model for the position of the weight at time $t$ is $s(t) = A \cos(\omega t)$ or $s(t) = A \sin(\omega t)$, where $A$ is the amplitude and $\omega$ is the angular frequency. Given that the amplitude is 4 inches and the frequency is $\frac{5}{\pi}$ cycles per second, we find the angular frequency by $\omega = 2\pi \times \text{frequency} = 2\pi \times \frac{5}{\pi} = 10$. Since the weight is initially pulled down, we use a cosine function with a negative amplitude, resulting in $s(t) = -4 \cos(10t)$.

Solve the Problem 5π\frac { 5 } { \pi }π5​ Cycles Per Second, Determine a Trigonometric Model That Gives the Pulled

Solve the Problem $\frac { 5 } { \pi }$ Cycles Per Second, Determine a Trigonometric Model That Gives the Pulled