Solutions to Free Undamped and Free Damped Motion Problems in Mass-Spring Systems

Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. A one-step sixth-order computational method is proposed in this paper for the solution of second order free undamped and free damped motions in mass-spring systems. The method of interpolation and collocation of power series approximate solution was adopted to generate a continuous computational hybrid linear multistep method which was evaluated at grid points to give a continuous block method. The resultant discrete block method was recovered when the continuous block method was evaluated at selected grid points. The basic properties of the method was also investigated and found to be zero-stable, consistent and convergent.