Consider a mass m that oscillates at the end of a spring having a spring constant k.The following second-order differential equation describes the vertical displacement y of this spring-mass system. Such a differential equation implies that mass m, once started, will simply oscillate up and down forever!This differential equation neglects the influence of frictional forces.Let us assume that there is a retarding force which is proportional to the velocity of motion where s is treated as a proportionality constant ().The aforementioned differential equation now becomes the following.Let and where.There are three possible types of solutions which depend upon the relative size of and, including the following:Overdamped if ,Critically damped if ,Underdamped or oscillatory if .Find the general solution for this differential equation, which describes the vertical displacement of this spring as a function of time t for 'overdamped' motion.

MCQs on Differential Equations.