=+with ????̃s defined as in (3.80). This expansion results from a decomposition in the basis of the complex conjugate modes z(s) of the damped system, with the associated eigenvalues ????s.

Show that, in case of light damping and well separate eigenfrequencies, the form

(a) can be approximated by the expression (3.29):

H(ω) = ∑n s=1 1

(

ω2 0s − ω2 + 2i????sωω0s

)

x(s)xT

(s)

????s

(P3.5.b)