From: W. Trevor King Date: Sun, 5 May 2013 18:45:34 +0000 (-0400) Subject: calibcant/discussion.tex: Fix simplifying multiplication for eq:peak-frequency X-Git-Tag: v1.0~261 X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=994ee2e9367a85bed19cda67872beefe2ee734b7;p=thesis.git calibcant/discussion.tex: Fix simplifying multiplication for eq:peak-frequency We can divide out all the things that *aren't* zero, and still have the right hand side be equal to zero. However, that doesn't mean that the new right hand side is the same as the old right hand side ;). --- diff --git a/src/calibcant/discussion.tex b/src/calibcant/discussion.tex index 8b0f9e2..5f40cc7 100644 --- a/src/calibcant/discussion.tex +++ b/src/calibcant/discussion.tex @@ -51,8 +51,8 @@ frequency of the resonant peak. 0 &= \deriv{f}{\PSD_f} = \frac{2G_{1f}f_\text{max}} {\p({(f_0^2-f_\text{max}^2)^2 + \beta_f^2 f_\text{max}^2})^2} - \p({2(f_0^2-f_\text{max}^2) - \beta_f^2}) - = 2(f_0^2-f_\text{max}^2) - \beta_f^2 \\ + \p({2(f_0^2-f_\text{max}^2) - \beta_f^2}) \\ + &= 2(f_0^2-f_\text{max}^2) - \beta_f^2 \\ f_\text{max}^2 &= f_0^2 - \frac{\beta_f^2}{2} \\ f_\text{max} &= \sqrt{f_0^2 - \frac{\beta_f^2}{2}} \;, \label{eq:peak-frequency}