Problem $3$

Two identical $0\mathrm{.}1$ kg blocks $($labeled $1$ and $2)$ were at rest on a nearly frictionless surface, connected by an unstretched spring whose stiffness is $100\frac{N}{m}.$ Then a constant force of $5$ N to the right was applied to block $2,$ and at a later time the blocks are in the new positions shown in the lower diagram.

$($a$)$At this later time, what is the total energy of the two block system?

$($b$)$ What is the translational kinetic energy of the two$-$block system?

$($c$)$ What is the speed of the center of mass of the two$-$block system?

$($d$)$ What is the vibrational kinetic energy of the tw$-$block system? Note: The spring is now stretched.