(1 point) Consider the initial value problem my" +cy' +163}: F0), yto) :0, 33(0) : 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force FOE)1 where the unit of force is the Newton (N). Assume that m = 2 kilograms. c = 8 Kilograms per second' k = 80 Newtons per meter, and F[t) = 60 cos(8t) Newtons. a. Solve the initial value problem. y(t) : help (formulas) a b. Determine the long-term behavior ofthe system. is thm y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive 400 values of t. For very large positive values of t: y(t) m help (formulas) cim yet lim [ g cos ( 6+) - 13 sin (6#) ) 20 4 -3 20 [4 sin ( 84) - 3 cos ( 8 8 ) ] ) lim 9 cos ( 6 + ) - 13 8 in(64) ] 20 f lim 20 [ 4 sin (24 ) - 3 cos ( @ + ) ] of does not exist does not exist Hence, lim yet) = does not exists Note : lim [ g cos ( 6+1 - 13 8in ( 6+]] = 0 20 and lim To [ 4 xin ( 8 +) - 3 (s ( Of ) = does net exists ( because sincot) and cos (at) are oscillatory function