As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t) = 8-t N/m. If the unforced mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 5 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x''(t) +x' (t) + (8-t)x(t) = 0; x(0)=5, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t = 0 for the displacement. k(t)=8-t heat x(t) = +... (Type an expression that includes all terms up to order 4.) 1 N-sec/m 2 kg x(t) x(0)=5 x'(0)=0