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

Question

Quizplus · Accepted Answer

The equation $d = 2 \sin 3t$ indicates a sinusoidal motion where the amplitude (maximum displacement) is 2 meters, indicating the object moves 2 meters away from the rest position at its peak. The angular frequency $\omega = 3$, and since the period $T = \frac{2\pi}{\omega}$, the period is $\frac{2\pi}{3}$ seconds. The frequency $f = \frac{1}{T} = \frac{3}{2\pi}$ oscillations per second.

An Object Is Attached to a Coiled Spring d=2sin⁡3td = 2 \sin 3 td=2sin3t

An Object Is Attached to a Coiled Spring $d = 2 \sin 3 t$