New Physics Old Mathematics
In this chapter you will see how the electric charge q varies with time in a circuit made up of an inductor L, a capacitor C, and a resistor R. From another point of view, we shall discuss how energy shuttles back and forth.between the magnetic field of the inductor and the electric field of the capacitor, while it is being gradually dissipated as thermal energy in the resistor. We have discussed oscillations before, in another context. In Chapter 16 we saw how isplacement x varies with time in a mechanical oscillating system made up of a block of mass m, a spring of spring constant k, and a viscous or frictional element such as oil; Fig. 16·15 shows such a system. We also saw how energy shuttles back and forth between the kinetic energy of the oscillating mass and the potential energy of the sQ.ring,being gradually dissipated as thermal energy. The parallel between these two idealized systems is exact, and the controlling
differential equations are identical. Thus, there is no new mathematics to be learned can simply change the symbols and give our full attention to the physics of the situation.