SOLUTIONS MANUAL
,
, CONTENTS
Chapter Page
2 ............................................................................................................................. 1
4 9
5 25
6 41
8 ...........................................................................................................................51
9 ...........................................................................................................................61
10 ..........................................................................................................................65
11 ..........................................................................................................................79
12 ..........................................................................................................................91
, Chapter 2
2.1 a. Spring constant, k: The change in the force per unit length change of the spring.
b. Coefficient of subgrade reaction, k:
k
Spring constant divided by the foundation contact area, k
A
c. Undamped natural circular frequency: n Rad/s
W
Where m = mass =
G
d. Undamped natural frequency: F n (in Hz)
2 m
Note: Circular frequency defines the rate of oscillation in term of radians per unit
time; 2π radians being equal to one complete cycle of rotation.
e. Period, T: The time required for the motion to begin repeating itself.
n
f. Resonance: Resonance occurs when 1
g. Critical damping coefficient: cc 2 km
W
Where k = spring constant; m = mass =
G
h. c c
Damping ratio: D =
cc 2 km
Where c = viscous damping coefficient; cc = critical damping coefficient
i. Damped natural frequency:
d n 1 D2
FD 1 D2 FN