Symon2-43

2-43 critically damped x = (x0 + (x0 - v0t)) e^(-γt)\n\nx = (0.2 + ct) e^(-70t)\nx = 0.2 e^(-70t)\n\n0.01 = 0.2 e^(-70t)\n0.01 e^(70t) = 0.2\ne^(-70t) = 0.05\n\nln(0.05) = -70t\n-0.76 = -70t\nt = 0.0109 s\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n1000 kg\n10 m \n∆x\nd\n\nNo. 1/2 mv^2 = mgh\nv^2 = 2gh\nv = sqrt(2gh)\nv = 14 m/s\n\nkx = mg\n(k = m/g)\n= (1000 kg)(9.81 m/s^2)\n\nk = 4.9 x 10^4 kg/s^2\n\nTo avoid overshoot,\n\nγ = v0/x0\n= 14 m/s\n0.2 m\n\nγ = 70 s^-1\n\nb = 5k\n2 m\n\nb = 8.2 m\n\nb = 1.4 x 10^5 kg/s