Solve the Problem $s = A \sin \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right)$

Multiple Choice

Solve the problem.
-The position (in centimeters) of an object oscillating up and down at the end of a spring is given by $s = A \sin \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right)$ at time $\mathrm { t }$ (in seconds) . The value of $\mathrm { A }$ is the amplitude of the motion, $\mathrm { k }$ is a measure of the stiffness of the spring, and $m$ is the mass of the object. Find the object's acceleration at time $t$ .

A) $a = - A \sin \left( \sqrt { \frac { k } { m } } t \right) \mathrm { cm } / \sec ^ { 2 }$
B) $a = - A \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \sin \left( \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t } \right) \mathrm { cm } / \mathrm { sec } ^ { 2 }$
C) $a = \frac { A k } { m } \cos \left( \sqrt { \frac { k } { m } } t \right) c m / \sec ^ { 2 }$
D) $a = - \frac { A k } { m } \sin \left( \sqrt { \frac { k } { m } } t \right) \mathrm { cm } / \mathrm { sec } ^ { 2 }$