Show that the equations of for this system are given by where J1, J2 are moments

Question

Show that the equations of for this system are given by where J1, J2 are moments of inertia, e is a damping constant, k is a spring constant, is a proportional constant, and is an input torque acting on Disk 2. Rewrite the equations of motion as a matrix second-order system. Assume that c = 0. Calculate the natural frequencies of the system. What are the physical meanings of these natural frequencies? Once you have the natural frequencies of the system, how do you determine the amplitudes of simple harmonic motion for 1 and ?

Explanation / Answer

e is the emf in the wire R is the resistance in the wire ? is the resistivity of the copper = 1.69x10-8Om L is the length of the wire = 0.520m A is the cross-sectional area of the wire = 0.500x10-3m The resistance is given by R = ?L/A, = ((1.69x10-8Om)(0.520m))/(p(0.500x10-3m)2) =1.11x10-2O. If B is the magnitude of the magnetic field through the loop, then according to Faraday's law e = (AdB)/(dt) where A is the area of the loop. The radius of the loop is r = L/2p Area is pr2 = (pL2)/(4p2) = L2/4p Then e = (L2/4p)(dB/dt) = ((0.520m)2/4p)(11x10-3T/s) =2.367 X 10 ^ -4 v The rate of the rmal energy generation is P = e2/R = [put the number in and u will have the answer. íx.H öx.H

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