(a) now take fy--mgf with ky if y< 0, 0 otherwise the new term ff represents the a spring-like force exerted on the mass by a floor at y-0. this force is only present when the height of the mass y(t) goes below zero. take k 104 n/m. now the mass should bounce off the floor; pick a range of t to show several bounces i. show that if the number of time points is too small, the rk2 solution is unstable and diverges to very large numbers (as in the first two problems in this homework set) ii. show that if the number of points is large enough to avoid the instability (e. g. 1000), there is still a significant error in the rk2 solution: the mass bounces to higher and higher heights, violating energy conservation (see newman sec. 8.5.2 for a discussion). the odeint solution does not have this problem iii. show that by using even more time points, the energy viola- tion in the rk2 solution can be made negligible. (b) change the floor force to otherwise where u = dy/de is the velocity of the mass. the new term γν represents a viscous damping force that reduces kinetic energy of the mass during bounces. try γ-10 n-s/m.