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

In summary, the conversation revolves around determining the amplitude, frequency, and time period of a complex waveform given by the equation VA=20 sin (50∏t) + 10 sin (100∏t). The conversation discusses using the standard formula for a time-varying sinusoid to determine the amplitude and radian frequency, and then using the formula T=1/f or T=2π/ω to find the period. It is also mentioned that there are no harmonics in either expression. The conversation ends with the clarification that there is an additional term added at a later stage.
  • #1
mammal
5
0

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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  • #2
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.
 
  • #3
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 waht the Fourier series is to be honest!
 
  • #4
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 waht 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.
 
  • #5
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!
 

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

1. What are complex waveforms?

Complex waveforms refer to signals or vibrations that are made up of multiple frequencies and amplitudes. They are considered more complex than simple waveforms, which have only one frequency and amplitude.

2. How are complex waveforms generated?

Complex waveforms can be generated through a variety of methods, including the combination of multiple simple waveforms, the use of modulation techniques, and the manipulation of existing waveforms using electronic devices.

3. What are some examples of complex waveforms?

Complex waveforms can be found in many natural phenomena, such as sound waves, ocean waves, and earthquake vibrations. They are also commonly used in electronic devices, such as music synthesizers and radio transmissions.

4. Why are complex waveforms important in science?

Complex waveforms are important in science because they can accurately represent real-world phenomena and can be used to study and understand the behavior of various systems. They are also used in many practical applications, such as in telecommunications and medical imaging.

5. How do scientists analyze complex waveforms?

Scientists use a variety of tools and techniques to analyze complex waveforms, such as Fourier analysis and spectral analysis. These methods help break down the complex waveform into its component frequencies and amplitudes, allowing for a better understanding of the signal.

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