Solve the problem.
-A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 7 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.
A) $y = - 5 \cos 7 \pi t$
B) $y = - 5 \cos 14 \pi t$
C) $y = 5 \cos 14 \pi t$
D) $y = 5 \cos \frac { 1 } { 7 } t$

Question

Quizplus · Accepted Answer

The correct model for the position of the weight at time $t$ is $y = - 5 \cos 14 \pi t$. This is because the amplitude of the motion is 5 inches (the distance the weight was pulled down), and the period is $\frac{1}{7}$ second, which means the frequency is $7$ cycles per second. The angular frequency $\omega$ is given by $2\pi \times \text{frequency}$, which equals $14\pi$. The negative sign indicates that the weight starts 5 inches below the equilibrium position.

Solve the Problem 17\frac { 1 } { 7 }71​ Second, Determine a Trigonometric Model That Gives the Position of Pulled

Solve the Problem $\frac { 1 } { 7 }$ Second, Determine a Trigonometric Model That Gives the Position of Pulled