Solve the problem.
-A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 6 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.
A) $s ( t ) = - 3 \cos 12 t$
B) $s ( t ) = 3 \cos 12 t$
C) $s ( t ) = 3 \pi \cos 6 t$
D) $s ( t ) = - 3 \cos \frac { 6 } { \pi } t$

Question

Quizplus · Accepted Answer

The correct model is $s(t) = -3 \cos(12t)$ because the amplitude is 3 (the initial displacement from equilibrium), and the angular frequency $\omega = 2\pi f$, where $f = \frac{6}{\pi}$ cycles per second, so $\omega = 2\pi \cdot \frac{6}{\pi} = 12$. The negative sign indicates the initial displacement direction (downward).

Solve the Problem 6π\frac { 6 } { \pi }π6​ Cycles Per Second, Determine a Trigonometric Model That Gives the Pulled

Solve the Problem $\frac { 6 } { \pi }$ Cycles Per Second, Determine a Trigonometric Model That Gives the Pulled