Section 4.7 is optional so there is no lecture video: if you’d like to know what happens when a finite elastic string is forced at one of its natural frequencies, then please take a look at the worked example in section 4.7 of the online lecture notes and the matlab generated movies.

Section 4.8  uses separation of variables to derive the normal modes of oscillation of a weighted string.



Section 4.9 describes the general solution of the wave equation.



Section 4.10 describes the derivation of D’Alembert’s Formula for the evolution of an infinite string.



Section 4.11 describes how a geometric interpretation of D’Alembert’s Formula may be exploited using a characteristic diagram.