Page 244 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 7 Problems 231

7-12 Determine the equation of motion and the natural frequency of oscillation about its
equilibrium position for the system in Prob. 7-5.
7-13 In Prob. 7-8, is given a small displacement and released. Determine the equation
of oscillation for the system.
7-14 For the system of Fig. P7-14, determine the equilibrium position and its equation of
vibration about it. Spring force = 0 when 9 = {).

Figure P7-14.
7-15 Write Lagrange’s equations of motion for the system shown in Fig. P7-15.

Figure P7-15.
7-16 The following constants are given for the beam of Fig. P7-16:
El El k
= N, = N
/ -’ ’ ml^ ml
K
K = 5 5 — , = 5N
mP
Using the modes (f)^ = x/I and (/>2 == sin(7TJc//), determine the equation of motion by

Lagrange’s method, and determine the first two natural frequencies and mode shapes.
E I , r

Figure P7-i6.

7-17 Using Lagrange’s method, determine the equations for the small oscillation of the bars
shown in Fig. P7-17.

Figure P7-17.