MOTION OF A HARMONIC OSCILLATOR UNDER
THE INFLUENCE OF A SEQUENCE OF A DELTA FUNCTION TYPE OF FORCES
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.