Page 127 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)
P. 127
124 Chapter 1 Fundamentals oF Vibration
1.22 An oil drum of diameter d and mass m floats in a bath of sea water of density r w as shown
in Fig. 1.78. Considering a small displacement x of the oil drum from its static equilibrium
position, determine the equivalent spring constant associated with the restoring force.
d
l Static
equilibrium
position
x
mg
FiGure 1.78 Oil drum floating in sea water.
1.23 Find the equivalent spring constant and equivalent mass of the system shown in Fig. 1.79
with references to u. Assume that the bars AOB and CD are rigid with negligible mass.
1.24 Find the length of the equivalent uniform hollow shaft of inner diameter d and thickness t that
has the same axial spring constant as that of the solid conical shaft shown in Fig. 1.80.
l 1 l
l 2 3
A O B
m 1 m 2
k t u
C
k 2
k 1
k 3
D
Liquid of m y
density r
d
FiGure 1.79 Springs and masses connected to a system of two rigid bars.
