On a frictionless horizontal surface, a $5\mathrm{.}00$ kg mass traveling at $20\mathrm{.}00$ m$/$s collides with and sticks to a $5\mathrm{.}00$ kg mass that is initially at rest. This system then runs into an ideal spring of force constant $25\mathrm{.}0$ N$/$m$.$ Using your knowledge of conservation of energy, conservation of momentum, and ideal spring $($a$)$ what will be the maximum compression of the spring? $($b$)$ how much mechanical energy is lost during this entire process? $($c$)$ during which parts of the process $($the collision and compression of the spring$)$ is the energy lost and why?