I have the following function which I must integrate:
F($\omega$) = $\int_{-\infty}^{\infty}\frac{1}{V\left[(\frac{\omega-\omega_{0}}{V})^{4}EI-\omega^{2}m\right]}d\omega$
With $V$ being velocity, $\omega_{0}$ the excitation frequency, $EI=EI(1+i\eta\omega)$ the stiffness with stiffness proportional damping and $m$ the mass. Basically I'm solving for the frequency dependent amplitude of the motion under a moving mass.
Solving for the roots with $\eta$ nonzero gives me 5 roots instead of 4 when $\eta$ is zero. For example for a certain set of parameters the zeroes are as follows (with $\omega_{0}=0$):
$\omega_{1,2} = 0; \omega{3} = 10.49-0.11i; \omega{4} = -10.49-0.11i; \omega{5} = 500.22i$
Thus I have 1 root of order 2 at the origin, and 3 simple roots of which there are two below the real axis and one above.
Now I have two questions:
- How do I handle the double zero root at the origin? (e.g. go around it?);
- Does it matter whether I take a semi-circle in the upper half-plane or the lower one? (as 'normally' with a inverse fourier transform you choose dependent on either the sign of $t$ or $x$, which is not possible in this case)
