Determine the Equation of the Graph $s ( t ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$

Multiple Choice

Determine the equation of the graph.
-The formula for the up and down motion of a weight on a spring is given by $s ( t ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$ . If the spring constant is 5 , then what mass $\mathrm { m }$ must be used in order to produce a period of 6 seconds?

A) $\frac { 4 } { \pi ^ { 2 } }$
B) $\frac { 45 } { \pi ^ { 2 } }$
C) $\frac { 5 \pi } { 2 }$
D) $\frac { 2 \pi } { 5 }$