The discussion revolves around calculating the amplitude of combined alternating currents in a circuit, specifically focusing on the mathematical approach to summing two sinusoidal functions. Participants explore various methods to derive the amplitude and the timing of its occurrence, engaging in both theoretical and practical reasoning.
Participants do not reach a consensus on the correct approach to calculating the amplitude and the angle of occurrence. There are multiple competing views on whether to treat the currents as phasors or to use a time-domain approach, and the discussion remains unresolved regarding the best method to apply.
Participants express varying levels of familiarity with differentiation and trigonometric identities, which may affect their ability to follow the proposed methods. There are also references to specific mathematical steps that remain unresolved, such as the correct application of the differentiation process and the interpretation of the results.
This discussion may be useful for students and practitioners in electrical engineering or physics who are dealing with alternating currents and sinusoidal functions, particularly those looking to deepen their understanding of combining waveforms and calculating amplitudes.
You almost had the correct answer in post #1. The trick I mentioned in post #17 is probably your simplest solution. B/A=2.5/10.33. It should be a simple matter to find ## \phi ## and write out the answer. And in the form ## y=C\cos(\omega t-\phi) ## the shift is to the right for positive ## \phi ##Enochfoul said:Thanks for all of your help and for the other guys help too. This question has been doing my head in.
Any chance you could have a look at the impedance question I posted. I can't decide if the final answer should be positive or negative.NascentOxygen said:It's right.
Either way, the answer should be the same.
I have the same question myself and have followed it up until this point, but i am confused as to wear the value 125 and -516.5 come from?Enochfoul said:Ok I've had another bash.
So If C = 2.5 sin 50t + 10.33 cos 50t
the dC/dt = 125 cos 50t - 516.5 sin 50t (diff of sin 50t is 50 cos 50t and diff of cos 50t is -50 sin 50t)
At a maximum dC/dt is 0
0 = 125 cos 50t - 516.5 sin 50t
rearrange and divide by cos 50t this give tan 50t = 2.5/10.33 giving 50t as 13.6 deg.
So 13.6 deg converted to radians would be 0.237.
0.237 ÷ 50 = 0.00474 which would be the time the amplitude of 10.6 would occur?
Using you tip of changing the graph to "Maximum of" it comes out as http://www4f.wolframalpha.com/Calculate/MSP/MSP72722a107agdc0he8ga0000405a140d63h2172g?MSPStoreType=image/gif&s=42&w=496.&h=33.
Im guessing this is correct then?
The function of time was differentiated. The values are a result of that operation.joe forrester said:I have the same question myself and have followed it up until this point, but i am confused as to wear the value 125 and -516.5 come from?
gneill said:The function of time was differentiated. The values are a result of that operation.
Differentiating trig functions sin and cos:
##\frac{d}{dt} Asin(ω t) = Aωcos(ω t)##
##\frac{d}{dt} Bcos(ω t) = -Bωsin(ω t)##