Longitudinal Vibrations of a Vertical Column by the Method of Laplace Transform Available to Purchase

An interesting illustrative problem in mechanics is the motion executed by a vertical rod or column when it suffers sudden loss of support at the bottom. A solution is presented by the method of Laplace transform in two alternative forms: one represents the motion as a superposition of free fall and two oppositely directed progressive waves equal in amplitude and form; the other, as a free fall and a pulse, initiated at the bottom and propagated up and down the column upon reflection at the ends.