George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3017
HW SET #2
Due 9/16/2026
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1) Derive the differential equation of motion for the system below
relating the output to input . Solve for (t) given (t)=us(t)
and plot x(t) vs. t. Assume I=1 Kg.m2, kT=25 N.m, and cT=6
N.m.sec.
2) Text Problem 4.42.
3) Text Problem 4.53.
4) Derive the equations of motion for the tractor-trailer system
shown below in terms of x1, x2, and the input torque T. Assume all the wheels roll without
slipping. Hint: You need the FBD of m1, the wheel I, and m2 to derive the equations of
motion. Also notice that x1=R where is the angular position of the wheel.
5) Derive a single differential equation for the rack and pinion system of Figure P4.65
relating the mass displacement x to the input torque T assuming a rigid shaft.
6) Find the transfer function X(s)/Y(s) for the system shown in Fig. P4.64.
7) Find the transfer function X2(s)/T(s) of the system in Problem 4.
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