The force constant of the spring is \(k\), the force on the particle is \(−kr\) and the potential (elastic) energy is \( V = \frac{1}{2} kr^2 \). It is difficult to imagine whether such forces actuall...The force constant of the spring is \(k\), the force on the particle is \(−kr\) and the potential (elastic) energy is \( V = \frac{1}{2} kr^2 \). It is difficult to imagine whether such forces actually exist in nature (the field of an electric dipole falls off as the cube of the distance - but the field is not radial, and the force is not a central force), and to that extent much of what follows is an exercise in mathematics more than in physics.
