Plot the effective potential using $U(r) = -\frac{m}{r^2}$ (Figures 10.3 and 10.4 in the textbook).

A particle of mass m and angular momentum of L experiences a central force that produces a potential of $U(r) = Ar^2$, where A is a positive constant. Plot the effective potential for this system.

A particle of mass m and angular momentum L moves in central force field that produces a potential that can be described by $U(r) = −Ae^{−\beta r^3}$ , where A and $\beta$ are constants. Plot the effective potential.

A particle of mass m and angular momentum of L experiences a central force that produces a potential of $U(r) = −Ar^3$ where A is a positive constant. Plot the effective potential for this system.