An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and
then released. Write an equation for the distance of the object from its rest position after t seconds.
-A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 7 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.
A) $y = - 5 \cos 14 t$
B) $y = 5 \cos 14 t$
C) $y = - 5 \cos \frac { 7 } { \pi } t$
D) $y = 5 \pi \cos 7 t$

Question

Quizplus · Accepted Answer

The correct model for the position of the weight at time $t$ seconds, given that it is pulled down 5 inches below the equilibrium position and has a frequency of $\frac{7}{\pi}$ cycles per second, is $y = -5 \cos(14t)$. This is because the amplitude is 5 (the distance it was pulled down), the cosine function is used for oscillatory motion, and the angular frequency $\omega$ is $2\pi f$, where $f = \frac{7}{\pi}$, so $\omega = 2\pi \cdot \frac{7}{\pi} = 14$. The negative sign indicates that the initial displacement is in the negative direction.

An Object Is Attached to a Coiled Spring 7π\frac { 7 } { \pi }π7​

An Object Is Attached to a Coiled Spring $\frac { 7 } { \pi }$