Determine the equation of the graph.
-A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $2 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?
A) $\mathrm { s } ( \mathrm { t } ) = \frac { 1 } { 2 } \sin \sqrt { \frac { 1 } { 10 } } \mathrm { t }$
B) $s ( t ) = 2 \sin \sqrt { \frac { 1 } { 5 } } t$
C) $s ( t ) = 2 \sin \sqrt { 5 } t$
D) $s ( t ) = 5 \sin \sqrt { 2 } t$

Question

Quizplus · Accepted Answer

The equation for the oscillatory motion of a spring-mass system is given by $s(t) = A \sin(\sqrt{\frac{k}{m}} t)$, where $A$ is the amplitude of the oscillation, $k$ is the spring constant, and $m$ is the mass. Here, $A = 2$, $k = 5$, and $m = 1$, so the equation becomes $s(t) = 2 \sin(\sqrt{5} t)$.

Determine the Equation of the Graph 2ft2 \mathrm { ft }2ft

Determine the Equation of the Graph $2 \mathrm { ft }$