Solve the problem.
-The formula for the up and down motion of a weight on a spring is given by $\mathrm { s } ( \mathrm { t } ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }$. If the spring constant is 5 , then what mass $m$ must be used in order to produce a period of 6 seconds?
A) $\frac { 5 \pi } { 2 }$
B) $\frac { 2 \pi } { 5 }$
C) $\frac { 45 } { \pi ^ { 2 } }$
D) $\frac { 4 } { \pi ^ { 2 } }$

Question

Quizplus · Accepted Answer

The period $T$ of a simple harmonic motion like a weight on a spring is given by $T = 2\pi\sqrt{\frac{m}{k}}$. Given $k = 5$ and $T = 6$, we solve for $m$: $6 = 2\pi\sqrt{\frac{m}{5}}$. Squaring both sides and solving for $m$ gives $m = \frac{45}{\pi^2}$.

Solve the Problem s(t)=sin⁡kmt\mathrm { s } ( \mathrm { t } ) = \sin \sqrt { \frac { \mathrm { k } } { \mathrm { m } } } \mathrm { t }s(t)=sinmk​​t

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