Question $1$

July $29,2024$

spring$01$be

Consider the following unforced, underdamped, spring system.

The spring with a constant of $13k\frac{g}{se{c}^2}$ is damped at $4k\frac{g}{sec}.$

After a $1$ kg mass is attached to the spring, it stretches to equal$-$

ibrium

From this equalibrium position, you pull the spring downward

$2\mathrm{.}00$ m from equalibrium as depicted in the graph.

Then you release the spring with an additional upward velocity

of $21\frac{m}{s}.$

Calculate the maximum displacement from equalibrium over the

subsequent oscillations.

Round your answer to two places, i$.$e$.3\mathrm{.}25.$

Hint: The graph is drawn to scale.