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.
-An object in simple harmonic motion has a frequency of $\frac { 5 } { 2 }$ oscillations per second and an amplitude of 3 feet. Write an equation in the form $\mathrm { d } = \mathrm { a } \sin \omega t$ for the object's simple harmonic motion.
A) $d = 3 \sin 5 \pi t$
B) $d = 3 \sin \frac { 5 \pi t } { 2 }$
C) $d = 3 \sin \frac { 5 t } { 2 \pi }$
D) $d = 3 \sin \frac { 2 t } { 5 }$

Question

Quizplus · Accepted Answer

The equation for simple harmonic motion is $d = a \sin(\omega t)$, where $a$ is the amplitude, and $\omega$ is the angular frequency. The angular frequency $\omega$ is related to the frequency $f$ by $\omega = 2\pi f$. Given $f = \frac{5}{2}$ oscillations per second, $\omega = 2\pi \times \frac{5}{2} = 5\pi$. Therefore, the equation is $d = 3 \sin(5\pi t)$.

An Object Is Attached to a Coiled Spring 52\frac { 5 } { 2 }25​

An Object Is Attached to a Coiled Spring $\frac { 5 } { 2 }$