If = 0, i. e. trivial solution. So, nontrivial solution is,
Materials
Damping ratio ( ) values
Concrete
0.05 to 0.07
Steel
0.01 to 0.02
Aluminum
0.001 to 0.01
Soil
0.1 to 0.2
There are three possibilities, Case 1) = So,
Table 8.1 Different values of Damping ratio ( ) Note: For soil values are high i.e. soil is a good damper.
= 0, i. e. trivial solution. 
) values 
= 
= (2m 
), 
) = (c/ 
). For different materials 
values are given in table 8.1.
) = 
, where 
is the undamped natural frequency of the system.
) 
values are high i.e. soil is a good damper. 
