Solution a(t=Ae Characteristic polynomia 入2+2cn入+ Roots 1 (-c+ 1),入2 General Solution(superposition) 入1t t a2e 入)t (-c+√c2-1)unt t Ae 1)wntSolution Try x(t) = Aeλt Characteristic Polynomial λ 2 + 2ζωnλ + ω 2 n = 0 Roots λ1 = ωn(−ζ + q ζ 2 − 1), λ2 = ωn(−ζ − q ζ 2 − 1) General Solution (superposition) x = A1e λ1t + A2e λ2t = A1e (−ζ+ √ ζ 2−1)ωnt + A2e (−ζ− √ ζ 2−1)ωnt 2