ANALOGY
MASS-SPRING MECHANICAL-ELECTRICAL SYSTEM Displacement x Velocity Diff Eqn:
dx =v dt d 2x m 2 + kx = 0 dt
LC CIRCUIT Charge q Current Diff Eqn:
dq =i dt
d 2q 1 L 2 + q=0 dt C
Mass m Spring constant k Frequency =
k m
Inductance L Inverse Capacitance 1 / C Frequency =
1 LC
Displacement: x = A cos (t + ) Velocity: v = A sin (t + ) Potential energy U = kx 2 = m 2 x 2
1 2 1 Kinetic energy K = mv 2 2
1 2 121 2 kx + mv = const 2 2
Charge: q = Q cos (t + ) Current: = i Q sin (t + ) Electrical energy Magnetic energy
q2 1 = CV 2 2C 2
12 Li 2
q2 1 2 + Li = const 2C 2
See Fig.30.15 of the text for a diagram of an LC circuit. The arrow in the figure shows the arbitrary direction chosen for a positive current. By convention, a current flowi...