The motion of a damped vertical spring system with a sudden inclusion of the mass is described by the following ordinary differential equation: mdt2d2y(t)+cdtdy(t)+ky(t)=mg;t0 where y(t)= displacement of the mass from the equilibrium position, t= time (s),m=5kg mass, and c= the damping coefficient (Ns/m). Assume, the damping coefficient c takes on three values of 2.5 (under-damped), 20 (critically damped), and 100 (over-damped). The spring constant k=20N/m and the acceleration due to gravity, g=9.81ms2. The initial displacement and the initial velocity both are zero (the spring was at rest before the inclusion of the 'mg' weight on it). Solve this equation by Classic Runge-Kutta method using suitable Python Program considering the time period 0t40sec. Plot the displacement versus time curves for each of the three values of the damping coefficient on the same curve. Also plot the velocity versus time curves in the similar manner. Estimate the peak value, peak time, rise time, overshoot and the final value of the displacement curves for each values of c. [Hints: If there is no oscillation found in the curve, overshoot will be zero, and the peak value and peak time will be undefined. However, by definition, the overshoot is, Overshoot=FinalValuePeakValueFinalValue100% However, rise time is defined as the time required for the curve to reach the 90% of its final value from the 10% of its final value.]