## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

$k = 4~N/m$
When all the energy in the system is in the form of kinetic energy, the kinetic energy is 8 J. Therefore, the total energy in the system is 8 J. When the spring is stretched or compressed by 2 meters, all the energy in the system is in the form of potential energy. We can find the spring constant. $U_s = E$ $\frac{1}{2}kA^2 = E$ $k = \frac{2E}{A^2}$ $k = \frac{(2)(8~J)}{(2~m)^2}$ $k = 4~N/m$