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

Solve the equation for exact solutions.
-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 $\mathrm { t }$ .

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

Correct Answer:

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