A mechanical system is shown in Figure P2.16, which is subjected to a known displacement x3 (t)

with respect to the reference.

(a) Determine the two independent equations of motion.

(b) Obtain the equations of motion in terms of the Laplace transform, assuming that the initial conditions are zero.

(c) Sketch a signal-flow graph representing the system of equations.

(d) Obtain the relationship T13 (s) between X1 (s) and X3 (s) by using Mason’s signal-flow gain formula. Compare the work necessary to obtain T13 (s) by matrix methods to that using Mason’s signal-

flow gain formula.

x3(1) Friction M1 b x1(t) K W M2 b x2(1) K2 FIGURE P2.16 Mechanical system.