Analyzing Complex Waveforms: Finding Amplitude, Frequency, and Time Period

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Discussion Overview

The discussion revolves around analyzing a complex waveform represented by the equation VA=20 sin (50∏t) + 10 sin (100∏t). Participants explore how to determine the amplitude, frequency, and time period of both the fundamental and harmonic components of the waveform. The scope includes homework-related problem-solving and mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem due to the presence of two parts in the complex waveform.
  • Another participant suggests performing the Fourier series on each term separately and notes that the frequencies are harmonically related.
  • A participant mentions calculating the frequency using ω=2πf and seeks assistance with amplitude and time period, indicating a lack of familiarity with Fourier series.
  • Another participant argues that Fourier analysis is unnecessary and suggests directly comparing the sinusoidal signals to the standard expression for a time-varying sinusoid to find amplitude and frequency.
  • One participant identifies the "20 sin (50∏t)" as the fundamental component and the "10 sin (100∏t)" as the second harmonic, mentioning an additional term for a later stage of the question.
  • A later reply indicates that the participant has figured out the answers, implying progress in understanding the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of Fourier analysis, with some advocating for its use while others argue it is not required. The discussion reflects differing levels of understanding regarding the analysis of the waveform.

Contextual Notes

Some participants express uncertainty about the Fourier series and its application, which may limit their ability to fully engage with the problem. There is also a mention of an additional term that complicates the analysis, but its implications are not fully explored in the discussion.

mammal
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Homework Statement



A complex waveform is given by the equation:

VA=20 sin (50∏t) + 10 sin (100∏t)

Determine the amplitude, frequency and time period of the fundamental and harmonic components.

Homework Equations



The sinusoidal voltage formula is v = V sin(2∏ft). In this formula f is the fundamental frequency.

The Attempt at a Solution



I have no idea how to approach this as there are two parts to the complex waveform.
 
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Do the Fourier series of each term separately, then see what terms can be combined.
Hint: one signal frequency is harmonically related to the other so you know ahead of time that such combinations can be effected.
 
I have worked out the frequency using ω=2πf on both terms and combining them, any ideas on the amplitude and time period?
I'm not sure what the Fourier series is to be honest!
 
mammal said:
I have worked out the frequency using ω=2πf on both terms and combining them, any ideas on the amplitude and time period?
I'm not sure what the Fourier series is to be honest!

I should have looked at the waveform more carefully. You don't need Fourier analysis at all.

You just have two sinusoidal signals added. So take the first, being 20sin(50πt), and compare it to the standard expression for a time-varying sinusoid, which is A sin(ωt). That gives you amplitude A and radian frequency ω immediately (you already got ω = 2πf correctly).

OK, now you know that T = 1/f, right? (Which can also be written T = 2π/ω). That gives you the period T.

There are no harmonics of either expression since both are sine waves. So go on to the second expression 10 sin(100πt) and do exactly the same thing. It too has no harmonics of course. So then you're done.
 
Apparently the "20 sin (50∏t)" is the fundamental part, and the "10 sin (100∏t)" is the second harmonic. There is also a further "+10 sin (150∏t)" added for a later stage of the question.
Thanks for the help I've been able to figure out the answers now!
 

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