Page 496 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 496
Chap. 14 Problems 483
T
h
T
Figure P14-3.
Xq. Establish the differential equation of motion for vertical oscillation.
14-4 Determine the differential equation of motion for the spring-mass system with the
discontinuous stiffness resulting from the free gaps of Fig. P14-4.
Figure P14-4.
14-5 The cord of a simple pendulum is wrapped around a fixed cylinder of radius R such
that its length is / when in the vertical position, as shown in Fig. P14-5. Determine
the differential equation of motion.
Figure P14-5.
14-6 Plot the phase plane trajectory for the undamped spring-mass system, including the
potential energy curve U(x). Discuss the initial conditions associated with the plot.
14-7 From the plot of U(x) vs. Jt of Prob. 14-6, determine the period from the equation
dx
= 4 /
•'n p [ E - U ( x ) ]
(Remember that E in the text was for a unit mass.)
