The Electrical Mechanical Analogy
Let us look a little closer at the analogy between the oscillating LC system of and an oscillating block – spring system. Two kinds of energy are involved in the block-spring system. One is potential energy of the compressed or extended
spring: the other is kinetic energy of the moving block. These two energies are given by the familiar formulas in the left energy column in Table The table also shows, in the right energy column, the two kinds of energy involved in LC oscillations. By looking across the table. we can see an analogy between the forms of the two pairs of energies-the mechanical energies of the block-spring system and the electromagnetic energies of the LC oscillator. Theequations for I’ and i at the bottom of the table help us see the details of the analogy. They tell us that q corresponds to x. and i corresponds to I’ (in both equations, the former is differentiated to obtain the latter). These correspondences then suggest that, in the energy expressions, I/C corresponds to k and L corresponds to m. Thus,q corresponds to .r,
i corresponds to 1′. and I/C corresponds to k,L corresponds to m, These correspondences suggest that in an LC ooscillator, the capacitor is mathematically like the spring in a block-spring system. and the inductor is like the block.
In Section 16-3 we saw that the angular frequency of oscillation of a (friction
The Energy In T.o Oscillating Sy stems Compared Block-Spring System LC OscillatorElement Energy Element Energy Spring Block Potential, !kx2 Kinetic. !mv2 v = dxldt Capacitor Inductor Electric. ~(\/C)q2Magnetic. ~Li2 ; = dqldt