The values of mass m, spring constant k, dashpot resistance c, and force f(t) are given for a mass-spring-dashpot system with external forcing function. Solve the initial value problem and construct the graph of the position function x(t). mx" + cx' + kx = f(t), x(0) = x'(0) = 0 X m = 1, k= 81, c=0; f(t) = sin 8t if Ost= 2n, f(t) = 0 if t> 2x A short table of laplace transforms Click the icon to view a short table of Laplace transforms. F(t) F(s) 1 on 1 - (s > 0) Solve the initial value problem. 2 (s > 0 ) n! 1 x(t) = 720 [1 - u(t - 2x)](9 sin (t) - sin (9t)) to (n 20) n + 1 (s > 0 ) r(a + 1) ta (a> - 1) a + 1 ( s > 0 ) 1 at ( s > a ) s - a S cos kt 5+ 12 (s > 0) K sin kt (s > 0 ) S cosh kt - K2 ( s > | kl) K sinh kt ( s > | k[ ) - as u(t - a) (s > 0 ) S n! e atn (s-a) + 1 (s > a) s - a e at cos kt (s - a) + k2 (s> a) k e at sin kt (s - a) + k2 (s > a)