Abstract

In this work, we set up the equation of motion of a mass according to Newton's second law of motion. The mass is tied to a spring under the simultaneous action of air resistance and a sequence of delta-function type of forces. It leads to second order in homogeneous linear differential equation. We solve the equation rigorously using residue theorem of complex variable. These solutions are abtained under differenct possibilities of parameters introduced in the problem.

We then develop a Mathematica program to plot three dimensional diagrams of the displacement as a function of time and natural frequency and under different parametric restrictions.