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) $\frac { 2 \pi } { 5 }$

Question

Quizplus · Accepted Answer

The period $T$ of a sinusoidal function like $s(t) = \sin(\sqrt{\frac{k}{m}}t)$ is given by $T = 2\pi \sqrt{\frac{m}{k}}$. Given $T = 6$ seconds and $k = 5$, we solve for $m$ by rearranging the formula: $m = \frac{T^2 k}{4\pi^2} = \frac{6^2 \cdot 5}{4\pi^2} = \frac{180}{4\pi^2} = \frac{45}{\pi^2}$.

Determine the Equation of the Graph s(t)=sin⁡kmts ( t ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }s(t)=sinmk​​t

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