ABSTRACT
This chapter considers other boundary value problems which are similar to the vibrating string problem. The intent here is to show the similarity in the approach to solving physical problems, which on the surface appear quite different but in fact have a similar mathematical structure. The chapter argues that the forces act along the rod axis and each cross-sectional area can move only along the rod axis. Such assumptions can be justified if the transverse dimensions are substantially smaller compared to the length of the rod and the forces acting on the rod are comparatively weak. The chapter discusses two physical situations which are typically encountered: waves created by a displacement and waves created by a pulse. It proposes a powerful Fourier method for solving partial differential equations for finite intervals. The chapter demonstrates how Laplace transform can be applied to solve heat, or generally a Partial Differential Equations equation.
