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 time dependent derivative of delta type of force. It leads to a second order first degree homogeneous differential equation. We solve the equation rigorously using residue theorem of complex variables. The solutions are obtained under different possibilities of parameters introduced. We then develop a Mathematica program to plot three dimensional diagrams of the displacement as a function of time and natural frequency under different parametric restrictions. |