Complex waveforms

Hedgecutter

Having some trouble with this question,

A complex wave is described by equation, y=100 sin ωt+30 sin(3ωt-∏/2)
A) on the same axis sketch and label,
1)one cycle of the fundamental waveform
2)the third harmonic
3) the complex waveform(y)

ω=2∏f
T=2∏/ω

Not sure where to start.
To sketch graph I need to find time, to get time I need frequency. Not sure how to find frequency from 100 sin ωt
as
Do I just treat ω as 2∏?

Michael Collins

Since you don't know what the frequency is you'll have to plot it in terms of ωt, instead of just t.

So on the x-axis you'll have values going from 0 up to 2pi, 2pi being the period of this waveform, can you see this?

The fundamental is the lowest frequency term. The first term has an angular frequency of ω, the second term has an angular frequency of 3ω.

So the first term is the fundamental in this case.

The second term has a frequency 3 times the fundamental, and therefore this is the third harmonic.

Hopefully this helps.

Hedgecutter

Michael Collins wrote: »

Since you don't know what the frequency is you'll have to plot it in terms of ωt, instead of just t.

So on the x-axis you'll have values going from 0 up to 2pi, 2pi being the period of this waveform, can you see this?

The fundamental is the lowest frequency term. The first term has an angular frequency of ω, the second term has an angular frequency of 3ω.

So the first term is the fundamental in this case.

The second term has a frequency 3 times the fundamental, and therefore this is the third harmonic.

Hopefully this helps.

Thanks for your help. I'll give that a go and see how I get on.