Consider the two cart$-$three spring system of section $11\mathrm{.}2,$ with equal mass and spring

constants. In natural units, m$=$k$=1.$ Suppose mass $1$ is displaced from equilibrium to the left by a

distance A$,$ while mass $2$ remains at its equilibrium. Both masses are then released and allowed

to oscillate without friction.

a$)$ Solve for the x$1($t$)$ and x$2($t$),$ the trajectories of the masses at all future times.

b$)$ Write it in normal coordinates and find their amplitudes