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February 14th, 2017, 11:54 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(3t45 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, 05:39 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,264 Thanks: 650 
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, 10:12 PM  #3 
Member Joined: Nov 2014 From: SG Posts: 55 Thanks: 1  
February 16th, 2017, 06:39 AM  #4 
Senior Member Joined: Sep 2015 From: CA Posts: 1,264 Thanks: 650  the method usually used is $\cos(a)\cos(b) =\dfrac 1 2 ( \cos(a+b) + \cos(ab))$ This gets you the standard 2x frequency, (a+b), which is usually filtered out, and the "beat frequency", (ab), which you're familiar with if you've ever tuned a guitar. 

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domain, express, phasors, solve, time 
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