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0593_C14_fm Page 510 Tuesday, May 7, 2002 6:56 AM

510 Dynamics of Mechanical Systems

14.5. Meirovitch, L., Elements of Vibration Analysis, McGraw-Hill, New York, 1975, 329 ff.
14.6. Meirovitch, L., Dynamics and Control of Structures, Wiley-Interscience, New York, 1990, 68 ff.

Problems

Section 14.2 Infinitesimal Stability

P14.2.1: A rod with length and mass m is supported by a frictionless pin and a torsion
spring at the support as represented in Figure P14.2.1. Determine the value of the minimum
spring modulus κ so that the rod is stable in a vertical equilibrium position while being
min
supported at its lower end.

θ

Torsion Spring
FIGURE P14.2.1
A pin-supported rod with a torsion
spring at the support.
P14.2.2: See Problem P14.2.1. Let the torsion spring modulus have a value of 0.8 κ min .
Determine the governing equation defining the static equilibrium position θ (in addition
to θ = 0).
P14.2.3: See Problem P14.2.1. Let the rod length be 1 m and let the mass be 2 kg. Determine
κ min .
P14.2.4: See Problems P14.2.1, P14.2.2, and P14.2.3. Determine the equilibrium angle θ
(aside from θ = 0) for the values of and m of Problem P14.2.3.
P14.2.5: Repeat Problem P14.2.4 if the rod length is 3 ft and the rod weight is 5 lb.

Section 14.3 A Particle in a Vertical Rotating Tube
P14.3.1: Consider the particle moving inside a smooth vertical rotating tube as discussed
in Section 14.3 and as depicted again in Figure P14.3.1. Determine the angular speed Ω
so that there is an equilibrium position at θ = 30° if the tube radius r is 18 in.

FIGURE P14.3.1
A vertical rotating tube with a smooth
interior surface and containing a particle P.