Page 182 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 5 Problems 169

5-51 Derive the equations of motion for the two masses in Fig. 5.8-5 and follow the parallel
development of the untuned torsional vibration-damper problem.
5-52 Draw the flow diagram and develop the Fortran program for the computation of the
response of the system shown in Prob. 5-4 when the mass 3m is excited by a
rectangular pulse of magnitude 100 lb and duration biryfinjk s.
5-53 In Prob. 5-31 assume the following data: /c, = 4 x 10^ Ib/in., k2 = ^ 10^ Ib/in.,
and mj = m2 = 100. Develop the flow diagram and the Fortran program for the case
in which the ground is given a displacement y = 10" sin irt for 4 s.
5-54 Figure P5-54 shows a degenerate 3 DOF. Its characteristic equation yields one zero
root and two elastic vibration frequencies. Discuss the physical significance that three
coordinates are required but only two natural frequencies arc obtained.

Figure P5-54.

5-55 The two uniform rigid bars shown in Fig. P5-55 are of equal length but of different
masses. Determine the equations of motion and the natural frequencies and mode
shapes using matrix methods.

Figure P5-55.

5-56 Show that the normal modes of the system of Prob. 5-54 are orthogonal.
5-57 For the system shown in Fig. P5-57 choose coordinates x, and X2 at the ends of the
bar and determine the type of coupling this introduces.

Figure P5-57.

5-58 Using the method of Laplace transforms, solve analytically the problem solved by the
digital computer in Sec. 5.5 and show that the solution is
= 13.01(1 - cosajj/) - 1.90(1 - COSCO2 O
y^^ = 16.08(1 - cosiOji) + 6.14(1 - cos 0^2 0