# Freq response of forced sinusoidal motion:

1. Nov 28, 2009

### H_man

The book I am currently reading derives the response of an electron to an applied sinusoidal field as:

1/[1 + 2i (w - wa)/g] = 1 / (1 + i delta)

where w and wa are the induced and resonance response frequencies and g the damping constant.

And delta = 2 (w - wa)/g

Up to this point there is no problem. But the book then states that the amplitude squared or power response has the form:

1/[1 + {2 (w - wa)/g}2 ] = 1 / (1 + delta2)

And here is the problem.... if you square the first equations listed you don't get what they give as the power response. I think the answer should be:

1 / (1 + 2 i delta - delta2)

Is there some assumption I am missing, its not just the imaginary term is missing the sign is wrong for the squared term??

Thanks for any help!

2. Nov 28, 2009

### Redbelly98

Staff Emeritus
For complex amplitudes, one squares the absolute value of the amplitude to get the power response.

3. Nov 30, 2009

Thanks!