Symon2-45

2-45\na) m\\ddot{x} + Kx = F_0\nx_t = x_0 + \\dot{x}t + \\frac{1}{2}a t^2\np = \\frac{b}{k} - \\frac{F_0}{k}\np = -\\gamma e^{\\beta t} + d\\nu\nt = e^{\\beta t}[c_1 e^{\\omega_n t} + c_2 e^{-\\omega_n t}]\n= e^{\\beta t}[c_1\\cos(\\omega_n t) + c_2\\sin(\\omega_n t)]\nX_n = A e^{\\beta t} \\cos(\\omega_n t + \\theta) \\{ \\cos\\theta = \\frac{e^{\\beta t} + e^{-\\beta t}}{2} \\}\nX_p = C\n\\dot{X_p} = 0\nKC = F_0\nC = \\frac{F_0}{k}\nX_p = \\frac{F_0}{k}\nx = x_0 + X_p\nx = A e^{\\beta t} \\cos(\\omega_n t + \\theta) + \\frac{F_0}{k}