Contour Integration

[Nusc]

Homework Statement

Find the poles for the integrals:
$$\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})}$$

One pole is at $$-(\gamma+\gamma_{n})$$.

Is there another one?


Also
$$\int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})} \frac{1}{s+\gamma+\gamma_{n}}$$
Similiarly, one pole is at $$-(\gamma+\gamma_{n})$$.

Is there another one? I just need to be sure.

Thanks

Homework Equations

The Attempt at a Solution

 

[Dick]

Poles are the values of the integration variable s where the denominator vanishes, right? I don't think -(gamma+gamma_n) is a pole. In both cases, it looks to me like you are getting a relatively complicated quadratic in s.

 

[Nusc]

Can you tell me what technique of integration I should use to evaluate this integral?

$$\noindent\(\frac{e^{s t}}{g^2+(s+\text{yn}+\gamma ) (s+\kappa )}\)$$

 

[Dick]

The ordinary residue theorem, I think. You can write that as e^(st)/((s-p1)(s-p2)) where p1 and p2 are the poles you get from solving the quadratic equation. It's straightforward in principle, but I don't know a simple way to write the nasty expressions you get from solving the quadratic. Where are you getting these problems??