Question

by syst D+2)x+(D + 2)y to the end of a spring, stretches it 4 inches. Initially, the mass ih from rest from a point 6 inches below the . Find the of motion g-32 ft/s2 for the xtt)-

Answer 1

D^2 x - Dy = t equation (1) (D + 2)x + (D + 2)y = 1 equation (2) Equation (1) times (D + 2) + Equation (2) times D D^2 (D + 2)x + D(D + 2)x = (D + 2)t + D middot 1 (D^3 + 2D^2 + D^2 + 2D)x = 1 + 2t (D^3 + 3D^2 + 2D)x = 1 + 2t A.E m^3 + 3m^2 + 2m = 0 m^2 (m + 2) + m(m + 2) = 0 (m + 2) (m^2 + m) = 0 (m + 2) (m^2 + m) = 0 m(m + 2) (m + 1) = 0 m = 0, -1, -2 C.F = c_1 + c_2 e^-t + c_2 e^-2t P.I = 1/(D^3 + 3D^2 + 2D) 1 + 2t = 1/2D [1 + (D^2 + 3D)]^-1 (1 + 2t) = 1/2D [1 - (D^2 + 3D) + ....] (1 + 2t) = 1/2D [1 + 2t - 3(2)]