My Math Forum Solve using phasors and express it in time domain

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 February 14th, 2017, 10:54 PM #1 Member     Joined: Nov 2014 From: SG Posts: 55 Thanks: 1 Solve using phasors and express it in time domain Perform the following using addition using phasors (a) V = 40sin2t + 60cos(3t-45 degree) How do I solve it if the angular frequency is difference? The youtube video teaches only if the angular frequency is the same For example , this link
 February 15th, 2017, 04:39 AM #2 Senior Member     Joined: Sep 2015 From: Southern California, USA Posts: 1,413 Thanks: 717 You can't really apply phasors to sinusoids of different frequencies. Their phase difference is time varying. are you sure that the second frequency shouldn't be $2t - 45^\circ ?$
February 15th, 2017, 09:12 PM   #3
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Quote:
 Originally Posted by romsek You can't really apply phasors to sinusoids of different frequencies. Their phase difference is time varying. are you sure that the second frequency shouldn't be $2t - 45^\circ ?$
Ya. is it possible to add them together if use other method?

February 16th, 2017, 05:39 AM   #4
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 Originally Posted by KaiL Ya. is it possible to add them together if use other method?
the method usually used is

$\cos(a)\cos(b) =\dfrac 1 2 ( \cos(a+b) + \cos(a-b))$

This gets you the standard 2x frequency, (a+b), which is usually filtered out, and the "beat frequency", (a-b), which you're familiar with if you've ever tuned a guitar.

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