Find the response to the input

1. Oct 4, 2007

kdinser

1. The problem statement, all variables and given/known data
for an LTIC system described by the transfer function
$$H(s)=\frac{s+2}{s^2+5s+4}$$

find the response to the following everlasting sinusoidal inputs:
5*cos(2t+30 degrees)

3. The attempt at a solution
$$H(jw) = \frac{jw+2}{4-w^2+j5w}$$

$$|H(jw)|=\sqrt{\frac{w^2+4}{(4-w^2)^2+25w^2}$$

$$\angle{H(jw) = TAN^{-1}\frac{w}{2} - TAN^{-1}\frac{5w}{4-w^2}$$

and that's where things go bad. if the input is 5cos(2t+30) and w=2 then the angle of H(jw) goes to infinity.

Where am I going wrong here?

2. Oct 4, 2007

wildman

What is the LaPlace transform of your input? How do you do a time domain convolution in the frequency domain?

3. Oct 5, 2007

kdinser

I found my error, I just plain forgot that arctan infinity was pi/2.