Solve.
-A formula for the up-and-down motion of a weight on a spring is given by $S = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$, where $\mathrm { k }$ is the spring constant, $\mathrm { m }$ is the mass, and $\mathrm { t }$ is the time. Solve the equation for $\mathrm { t }$.
A) $t = \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \sin \left( \frac { 2 } { \mathrm {~S} } \right)$
B) $t = \frac { m } { \sqrt { k } } \arcsin \left( \frac { S } { 2 } \right)$
C) $t = \frac { \sqrt { k } } { m } \arcsin \left( \frac { s } { 2 } \right)$
D) $t = \frac { m } { \sqrt { k } } \sin \left( \frac { S } { 2 } \right)$

Question

Quizplus · Accepted Answer

To solve for $t$, first isolate the sine term: $S = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$ becomes $\sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \mathrm { t } \right) = \frac { S } { 2 }$. Then, apply the inverse sine ($\arcsin$) to both sides to solve for $t$, resulting in $t = \frac { m } { \sqrt { k } } \arcsin \left( \frac { S } { 2 } \right)$.

Solve -A Formula for the Up-And-Down Motion of a Weight S=2sin⁡(km)tS = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }S=2sin(mk​​)t

Solve
-A Formula for the Up-And-Down Motion of a Weight $S = 2 \sin \left( \frac { \sqrt { \mathrm { k } } } { \mathrm { m } } \right) \mathrm { t }$