# Sketching Complex Waveform with Equation y=100sinωt+30sin(3ωt-π/2)

• anthonyk2013
In summary, the conversation discusses how to sketch a complex wave described by the equation y=100 sin ωt+30 sin(3ωt-∏/2) and how to label the fundamental waveform, the third harmonic, and the complex waveform on the same axis. The conversation discusses using ##\omega\, t## as the x coordinate and suggests choosing ##\omega = 1## for simplicity. The conversation also clarifies that there is no solving involved, only plotting.
anthonyk2013
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∏?

Last edited:
No, you treat ##\omega\, t## as the x coordinate.

BvU said:
No, you treat ##\omega\, t## as the x coordinate.

Ok so I have ωt, ωt/2, ωt/3 along my x-axis for my time coordinates ?

Last edited:
No, just ##\omega \, t##

If you still feel uncomfortable, choose ##\omega = 1##, make the y, t plot and then rename the t axis to ##\omega t## axis !

BvU said:
If you still feel uncomfortable, choose ##\omega = 1##, make the y, t plot and then rename the t axis to ##\omega t## axis !

Where I'm getting confused is I'm used to solving the likes of 100 sin (100 ∏ t)

from there you get time=20ms, so you can plot the time axis up to 20ms.

I don't understand how to plot ωt

Perhaps I confused you earlier on, sorry. There is no solving involved, just plotting. One period in A1 -- so from ##100 \, \omega\, t=0 ## to ##100\, \omega\, t=2\pi ##

#### Attachments

• Sine100wt.jpg
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I understand now cheers.

## 1. What is the purpose of sketching complex waveforms?

The purpose of sketching complex waveforms is to visually represent a mathematical equation that describes the behavior of a wave. This can help in understanding the properties and characteristics of the wave, such as amplitude, frequency, and phase.

## 2. How do you determine the amplitude of a complex waveform?

The amplitude of a complex waveform is determined by the coefficient in front of the trigonometric function. In the given equation y=100sinωt+30sin(3ωt-π/2), the amplitude for the first term is 100 and for the second term is 30.

## 3. What does the ω symbol represent in the equation?

The symbol ω, also known as omega, represents the angular frequency of the wave. It is related to the frequency of the wave by the equation ω = 2πf, where f is the frequency in hertz (Hz).

## 4. What is the significance of the phase shift in the second term of the equation?

The phase shift, represented by -π/2 in the second term of the equation, indicates a shift in the starting point of the wave. In this case, the waveform will start at a point that is π/2 radians behind the first term, resulting in a different shape of the waveform.

## 5. Can complex waveforms be used to model real-world phenomena?

Yes, complex waveforms can be used to model a variety of real-world phenomena, such as sound waves, electromagnetic waves, and even biological rhythms. By adjusting the parameters in the equation, complex waveforms can accurately represent the behavior of these phenomena.

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