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.
-$d = 3 \cos 5 \pi t$ meters
A) displacement $= 3$ meters; period $= \frac { 2 } { 5 }$ seconds; $\mathrm { f } = \frac { 5 } { 2 }$ oscillations/second
B) displacement $= 3$ meters; period $= \frac { 5 } { 2 }$ seconds; $\mathrm { f } = \frac { 2 } { 5 }$ oscillations/second
C) displacement $= 3$ meters; period $= \frac { 2 } { 5 } \pi$ seconds; $\mathrm { f } = \frac { 5 } { 2 \pi }$ oscillations/second
D) displacement $= - 3$ meters; period $= \frac { 5 } { 2 }$ seconds; $\mathrm { f } = \frac { 2 } { 5 }$ oscillations/second

Question

Quizplus · Accepted Answer

The equation $d = 3 \cos 5 \pi t$ describes a cosine function where the amplitude (maximum displacement) is 3 meters, indicating the object moves 3 meters from its rest position. The angular frequency $\omega = 5\pi$ radians/second, and the period $T = \frac{2\pi}{\omega} = \frac{2\pi}{5\pi} = \frac{2}{5}$ seconds, which is the time it takes for one complete oscillation. The frequency $f = \frac{1}{T} = \frac{5}{2}$ oscillations/second, is the number of oscillations per second.

An Object Is Attached to a Coiled Spring d=3cos⁡5πtd = 3 \cos 5 \pi td=3cos5πt

An Object Is Attached to a Coiled Spring $d = 3 \cos 5 \pi t$