Question

I

6. 16 points] A goat weighing 64 pounds stretches a spring by 3.2 feet. The goat is attached to a viscous damper with a damping constant of 4 lb-sec/ft purchased from Goat Dampers H Us. The goat is pulled down by another 4.8 feet and released a) Write the DE governing the displacement of the goat b) Find the displacement of the goat as a function of time c) Is the goat overdamped, underdamped, or something else?

Answer 1

"Consider the above given that A goat weighting = 64 pounds stretches a spring = 3.2 feets bending the force in figure wmg - fv -k(x_1 + x_2) = ma w = kx_1 ma = -N - kx_2 m d^2x_2/dt_2 + y dx_2/dt + kx_2 = 0 subtitle the all value m = 64/32 = 2 y/m = 2 k/m = 10 d^2x_2/dt^2 + 2dx_2/dt + 10x_2 = 0 find out the roots r^2 + 2r + 10 = 0 r = -b plu or minus srare root b^2-4ac/2a = -2 plus or minus squareroot 4-4(0)/2 = -1plus or minus 3i x_2 = c_e at cos 3t + c_2e^t sin t since x^2 < y_m k then the system is a under damped is the goat is under ""damped"""