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

[mammal]

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.

 

[rude man]

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.

 

[mammal]

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!

 

[rude man]

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.

 

[mammal]

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!