the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest
position after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that
-a = 5; T = 3 seconds

A) $\mathrm { d } = - 5 \cos \left( \frac { 1 } { 3 } \pi \mathrm { t } \right)$
B) $d = - 3 \cos \left( \frac { 2 } { 5 } \pi t \right)$
C) $d = - 5 \sin \left( \frac { 2 } { 3 } \pi t \right)$
D) $\mathrm { d } = - 5 \cos \left( \frac { 2 } { 3 } \pi \mathrm { t } \right)$

Question

the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest
position after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that
-a = 5; T = 3 seconds

A) $\mathrm { d } = - 5 \cos \left( \frac { 1 } { 3 } \pi \mathrm { t } \right)$
B) $d = - 3 \cos \left( \frac { 2 } { 5 } \pi t \right)$
C) $d = - 5 \sin \left( \frac { 2 } { 3 } \pi t \right)$
D) $\mathrm { d } = - 5 \cos \left( \frac { 2 } { 3 } \pi \mathrm { t } \right)$

Quizplus · Accepted Answer

The displacement in simple harmonic motion can be described by $d = a \cos(\omega t)$ or $d = a \sin(\omega t)$. The angular frequency $\omega$ is given by $\omega = \frac{2\pi}{T}$. For T = 3, $\omega = \frac{2\pi}{3}$. Since the object is pulled down and released, the cosine function is appropriate, making the equation $d = -5 \cos \left( \frac{2}{3} \pi t \right)$.

The Motion Is Simple Harmonic with Period T, Write an Equation