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| Complex frequency of an exponentially damped sinusoidal function |
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| T. Mandresy Billy:
In my textbook, Engineering Circuit Analysis 8.Ed by William H. Hayt (Chapter 14, Section 14.1 page 536) I stumbled across a section explaining the complex frequency. The goal is to cover the concept of complex frequency when it comes to exponentially damped sinusoidal functions. https://my.pcloud.com/publink/show?code=XZPPlg7ZngPpIC2dhafb9scO3EVjpHvok5py HOW DID THIS HAPPEN? How did eσt become ejσt out of the blue? And why did ej(ωt) become ej(jωt) ? Any help would be much appreciated. |
| Wimberleytech:
It comes from Eulers relationship |
| T. Mandresy Billy:
Thanks for stopping by. I know this Euler's relationship. The real mystery is below. Look at it and you will find, from the mathematical expressions that: exp(σt) become exp(jσt). How did this happen? why did exp(jωt) become exp(jjωt)? AN ADDITIONAL j SUDDENTLY APPEARS. |
| Wimberleytech:
Sorry...when the image came on my screen i did not see the last line. It is just algebra to get to the last step. First get all terms in the form of e^x and then recombine. There is a typo in the book. That accounts for the extra j. It should not be there. |
| T. Mandresy Billy:
Glad to be reassured it was just a typo. I will email the editor about this then. |
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