(Solved): Consider the following unforced, damped, spring system. The spring constant is \( 408 \mathrm{~kg} ...

Consider the following unforced, damped, spring system. The spring constant is \( 408 \mathrm{~kg} / \mathrm{sec}^{2} \) and the system is critically damped for a \( 98 \mathrm{~kg} \) mass. The equalibrium point for a spring is where we place the origin. Initially, the \( 7.00 \mathrm{~m} \) long spring is stretched to equilibrium by the masss. This means \( x(0)=0 \). The spring is subjected to an initial impulse of \( 24.00 \mathrm{~m} / \mathrm{s} \), compressing the spring upward. Calculate the maximum displacement from equalibrium that the spring is compressed Round your answer to two places, i.e. \( 3.25 \).