An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that
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.
-$$\mathrm { a } = 5 ; \quad \mathrm { T } = 10 \text { seconds }$$
A) $d = 5 \cos ( 10 t )$
B) $d = - 5 \cos ( 10 t )$
C) $ d = - 5 \cos \left( \frac { \pi } { 5 } t \right)$
D) $d = 5 \cos \left( \frac { \pi } { 5 } t \right)$

Question

Quizplus · Accepted Answer

The equation for simple harmonic motion is $d = a \cos \left( \frac{2\pi}{T} t \right)$. Given $a = 5$ and $T = 10$, the equation becomes $d = 5 \cos \left( \frac{\pi}{5} t \right)$. Since the object is pulled down initially, the displacement is negative, hence the equation is $d = -5 \cos \left( \frac{\pi}{5} t \right)$.

An Object Attached to a Coiled Spring Is Pulled Down a=5;T=10 seconds \mathrm { a } = 5 ; \quad \mathrm { T } = 10 \text { seconds }a=5;T=10 seconds

An Object Attached to a Coiled Spring Is Pulled Down $\mathrm { a } = 5 ; \quad \mathrm { T } = 10 \text { seconds }$