
6.15. Consider a single degree-of-freedom system with mass m, damping coefficient c, and no spring
element. The mass is subjected to an excitation force given by m
¨
X(t), where
¨
X (t) is a stationary white
noise random process of intensity S
0
m
2
/s
3
. Determine
(a) the complex frequency response function H(ω) for the response velocity V (t), and
(b) the power spectral density S
V V
(ω) and the mean-square value E{V
2
} of the stationary velocity
response, where V (t) =
˙
X(t).
Solution: (a) From the problem statement, the equation of motion is given by
m
¨
Y (t) + c
˙
Y (t) = mX(t).
Velocity is
˙
Y (t) , and its Fourier transform is iωY (ω) , where Y (ω) is the Fourier ...