Symon2-57

2-57 mx + bx + kx = F \\x(0) = 0, v(0) = 0, F = Asinwt + Bsinwt \\ a) mx_n + bx_n + kx_n = F_n \\ F_i = Asinwt \\ x_0 = 0 \\ x(1) = 0, v(0) = 0) \\ x_p = K_r coswt + K_s sinwt \\ x_r = - \\omega^2 K_i sinwt + \\omega^2 K_s coswt \\ x_p = K_r coswt - 3K_i sinwt \\ x_r = -3K_i \\ k = b / m \\ coswt = -w^2 k_1 + k_2 \\ k_1 = 0 \\ k_2 = 2Yx = 0 \\ k_r = -K_r + 2k^2_K_2 = 0 \\ 2w^2 k_1 + 2w^2 k_2 = 3 \\ K_r = 0 \\ k_1 = 0 \\ sinwt = -\surt{w^2 k_1 - 4w^2 k_2} = A/m \\ K^2 = + \\ K_s \\ K_{r2} = -3 \\ \\ -K_2 + k/3K_1 = 0 \\ 2v^2K_2 + 2w^2 K_1 + 4w^2 K_2 = 0 \\ -4 -2^2 k_1 = K_r = 0 \\ 3/2 m + K = 0 \\ 2 - b = 1 \\ k_1r = 1 \\ .smwt = .m_2 = 0.3 \\ K_{12} = -K = \\ K_{12} + K_i + K_2 \\ K_{12} = K_{1i} - K = 0 x_p = \\frac{3A}{2m \\omega^2} = \\frac{2b}{3K + \\frac{3}{4}} \\ \\ x(t) = x_p + x_n(t) \\ = \\frac{3}{2m} \\left[\\cos(2/3wt) + \\sin(3wt)\\right] \\ -3\\int_{\\frac{A}{m}} \\left[\\surd \\frac{m}{K} \\right] = 0 \\ \\ -3 = - \\ind{K_i},1.0 =0 \\ K_{22} + 3C_{12} + \\omega)^2 = -6 i+2j \\ K_{12} + m_2\\frac{\\left[2p t\\right]} + 2 + \\frac{m}{3} + K_n \\ = = K_{x(t)} x(t) = e^{\\frac{-K}{3}} \\left[C_1 + \\frac{4}{10^3} \\right] + \\left(x_1(t) + x_2(t)+ \\frac{12v}{3^{1/2}} \\right) \\ + K^2 \\it{3}At \\cdots 0.0 \\ = K_{x1}(xin x_n) = \\frac{3A }{34 } x_{(0)} \\ = K^t_{12} \\left(\\ \frac{1+}322 \\right) + \\frac{5A}{12A \\}\ (3) \\ \\ \\ K = A e^{-kt}}) b) X(t) = \\frac{1}{m}\\left[-\\frac{3}{4} \\cos(\\omega t) \\cdot \\frac{B_0}{4} (\\cos(\\omega t)+\\sin(2\\omega t)]}, t >> 0\\n\\n\\n\\frac{3}{4} \\cos(\\omega t) = \\frac{B_0}{4}(\\cos(\\omega t)+\\sin(2\\omega t))\\n\\nB = \\frac{51}{0}\\nA = \\frac{\\cos(\\omega t)}{\\sin(2\\omega t)}