Solve the problem.
-A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.
A) $s ( t ) = - 6 \cos 2 \pi t$
B) $s ( t ) = 6 \cos \frac { 1 } { 2 } t$
C) $s ( t ) = 6 \cos 4 \pi t$
D) $s ( t ) = - 6 \cos 4 \pi t$

Question

Quizplus · Accepted Answer

The correct model is $s(t) = -6 \cos 4\pi t$. The amplitude is 6 inches (the initial displacement), and since the period $T = \frac{1}{2}$ second, the frequency $f = \frac{1}{T} = 2$ Hz. The angular frequency $\omega = 2\pi f = 4\pi$ radians per second. The negative sign indicates the initial displacement is in the opposite direction of the positive direction assumed for $s(t)$.

Solve the Problem 12\frac { 1 } { 2 }21​ Second, Determine a Trigonometric Model That Gives the Position of Pulled

Solve the Problem $\frac { 1 } { 2 }$ Second, Determine a Trigonometric Model That Gives the Position of Pulled