MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES — Edward Purcell & David Morin
Physics — E&M · underdamped-motion
Problem
A second-order homogeneous linear differential equation can be written in the general form of
x¨+2αx˙+ω02x=0,
where α and ω0 are constants. (For the series RLC circuit in Section 8.1, Eq. (8.2) gives these constants as α=R/2L and ω02=1/LC.) From Problem 8.2 we know that there are two independent exponential solutions to this equation. Find these two solutions, and then show that, in the underdamped case where α<ω0, the general solution can be written in the form of Eq. (8.10).