Aparticle of mass m and charge +q is constrained to move on the x-axis. two identical particles of charge-a are held fixed on the y-axis at y = ±1·(the two fixed charges are equal and opposite to the moving charge.) (a) write (and sketch) the potential energy u(x) of the moving charge, and discuss the types of motion for all possible values of total energy e. (for example, bounded vs unbounded, number of turning points, etc.) oscillations about this equilibrium necessarily "small") to the right. find the equation of the phase-space diagram (v vs. x). (b) show that the origin is a stable equilibrium point, and find the effective spring constant of (c) now assume that the particle is initially at the origin and is given a velocity vo (not and sketch the phase portrait as completely as you can (d) find the escape velocity ve , and the find the corresponding equation of the separatrix (i. e., the phase-space equation that separates the bounded cyclic motion from the unbounded motion)