ABSTRACT
This chapter considers the Laplace transform method to obtain solutions to the various boundary value problems. The problems covered are displacement of a beam with an in-span spring to a uniform static load, response of a two degree-of-freedom system to external forces and initial conditions, one-dimensional heat conduction in rectangular coordinates with nonhomogeneous boundary conditions and an initial condition, and diffusion in polar coordinates with time-dependent boundary conditions. They also include response of a semi-infinite beam to a time-dependent boundary condition, traveling point load on a semi-infinite string, longitudinal vibrations of a bar with an attachment at a free end, response of a beam with an in-span mass to a dynamic load, and response of a Timoshenko beam to a dynamic load. The ordinary and partial differential equations, boundary conditions, and initial conditions that appear in each of these examples are summarized.
