6. A certain model of the motion light plastic ball tossed into the air is given by mx+cx+mg=0,x(0)=0,x(0)=v0. Here m is the mass of the ball, g=9.8m/s2 is the acceleration due to gravity and c is a measure of the damping. Since there is no x term, we can write this as a first order equation for the velocity v(t)=x(t) : mv+cv+mg=0. a. Model this problem using Simulink. b. Determine how long it takes for the ball to reach it's maximum height? c. Assume that c/m=5s1. For v0=5,10,15,20m/s, plot the solution, x(t), versus the time. d. From your plots and the expression in part b., determine the rise time. Do these answers agree? e. What can you say about the time it takes for the ball to fall as compared to the rise time? f. If an input 3sin(2t+pi/3) is added to the dynamic system, plot the olutions with v0=5m/s,c/m=1,2,3,4,5. And discuss the system responses. mx+cx+mg=3sin(2t+3)