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) $t = \frac { \sqrt { k } } { m } \arcsin \left( \frac { S } { a } \right)$

Question

Quizplus · Accepted Answer

To solve for $t$, you isolate it on one side of the equation. Starting with $S = a \sin \left( \frac { \sqrt { k } } { m } \right) t$, you divide both sides by $a$ to get $\frac{S}{a} = \sin \left( \frac { \sqrt { k } } { m } \right) t$. Then, you apply the inverse sine ($\arcsin$) to both sides to get $\arcsin\left(\frac{S}{a}\right) = \frac { \sqrt { k } } { m } t$. Finally, to solve for $t$, you multiply both sides by $\frac{m}{\sqrt{k}}$ to get $t = \frac { m } { \sqrt { k } } \arcsin \left( \frac { S } { a } \right)$.

Solve the Problem S=asin⁡(km)t\mathrm { S } = \mathrm { a } \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }S=asin(mk​​)t

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