Damped mechanical systems provide a wonderful laboratory in which to explore spectral properties of non-self-adjoint differential operators. In this talk we shall describe a variety of our recent investigations in this area, touching on theory (eigenvalue bounds for a model of a conducting wire vibrating in a magnetic field), computation (careful pseudospectral discretizations for analysis of transient energy behavior), and experiment (careful physical measurements of eigenvalues from the monochord in our string vibration lab).

[Joint work with Steve Cox, Jeff Hokanson, and Walter Kelm]