(1 point) A 2kg mass is attached to a spring hanging from the ceiling. This causes the spring to stretch 20 cm. The system has a friction constant of 10. After coming to a stop at its new equilibrium, the mass is pulled 50 cm further toward the floor (i.e. y(0) = .5) and released subject to a driving force function F(t) = .3 cos(t). Recall that we can calculate k when we know the displacement d caused by a mass m because d mg == [use g = 9.8 m/sec²]. The differential equation to solve has = 98 The steady state solution yp is 36/11645cos(t)+3/9316sin(t) The actual solution y(t) to the ivp is e^(-5/2t)[.5cos(sqrt(171)/2t)+.2sin(sqrt(171)/2t)]+36/11645cos(t) To illustrate that yp is steady-state and y, is transitory, Calculate the value lyp (3) - y(3)| = 7 In other words the solution y(t) is quickly converging to y,(t) and so the effects of the initial stretching is quickly dissipated.