Problem $7$: $[15$ points$]$ Given are the energies $E_1$ and $E_2,$ and the potential $U$ pictured below. Describe the possible trajectory$/$trajectories and draw a corresponding $(x,x^{})$ diagram, of a particle subject to this potential and having a total energy of

$($a$)E_1,$

$($b$)E_2,$ and

$($c$)E_3.$