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 = 17; T = 5 seconds
A) $d = - 17 \sin \left( \frac { 2 } { 5 } \pi t \right)$
B) $d = - 17 \cos \left( \frac { 2 } { 5 } \pi t \right)$
C) $d = - 17 \cos \left( \frac { 1 } { 5 } \pi t \right)$
D) $\mathrm { d } = - 5 \cos \left( \frac { 2 } { 17 } \pi \mathrm { t } \right)$

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 = 17; T = 5 seconds 
A) $d = - 17 \sin \left( \frac { 2 } { 5 } \pi t \right)$
B) $d = - 17 \cos \left( \frac { 2 } { 5 } \pi t \right)$
C) $d = - 17 \cos \left( \frac { 1 } { 5 } \pi t \right)$
D) $\mathrm { d } = - 5 \cos \left( \frac { 2 } { 17 } \pi \mathrm { t } \right)$

Quizplus · Accepted Answer

The correct equation for the displacement d in simple harmonic motion, where the motion starts from the maximum displacement (a = 17) in the negative direction (down), is given by $d = -a \cos\left(\frac{2\pi}{T}t\right)$. Substituting $a = 17$ and $T = 5$ seconds into the equation gives $d = -17 \cos\left(\frac{2\pi}{5}t\right)$, which matches choice B.

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