Module 7 :
Design of Machine Foundations
Lecture 31 : Basics of soil dynamics [ Section 31.2 :
Different modes of vibration; Undamped
]
If
= 0, i. e. trivial solution.
So, nontrivial solution is,
+ k = 0.
where,
is the natural frequency of the system (rad/sec).
General solution is,
…
---------(2)
Applying boundary conditions,
Substituting in equation (2),
As
are real values ,
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= 0, i. e. trivial solution. 
+ k = 0. 
is the natural frequency of the system (rad/sec). 
…
are real values , 
