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

Multiple Choice

Solve the problem.
-The formula for the up-and-down motion of a weight on a spring is given by $$\mathrm { S } = \mathrm { a } \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$$
where a is the radius of the circle, $\mathrm { k }$ is the spring constant, $\mathrm { m }$ is the mass, and $\mathrm { t }$ is the time. Solve the equation for t.

A) $t = \frac { m } { \sqrt { k } } \arcsin \left( \frac { S } { a } \right)$
B) $t = \frac { m } { \sqrt { k } } \sin \left( \frac { S } { a } \right)$
C) $t = \frac { \sqrt { k } } { m } \sin \left( \frac { a } { S } \right)$
D) $t = \frac { \sqrt { k } } { m } \arcsin \left( \frac { S } { a } \right)$