Plotting Phasor representations of functions

[VinnyCee]

Homework Statement

Plot the following for x = 0 to 8:

This is part of a larger engineering problem, but I am stuck here, I have no idea how to plot a phasor.

The original function is:

$$y(x,\,t)\,=\,2\,cos\left(\frac{\pi}{6}\,t\,-\,\frac{\pi}{4}\,x\right)$$

Homework Equations

The Attempt at a Solution

And the phasor representation...

$$\tilde{Y}(x)\,=\,2\,e^{j\left(-\frac{\pi}{4}\,x\right)}$$

How do I plot that?!?

 

[Kurdt]

The plot will be a circle in the complex plane of radius 2. The phasors will be points on the circle with angle given by $- \frac{\pi}{4} x$.

 

[Moetasim]

I would suggest starting by understanding what a phasor representation is and how it relates to the original function. A phasor is a complex number that represents the magnitude and phase of a sinusoidal function. In this case, the phasor \tilde{Y}(x) represents the amplitude and phase of the cosine function in the original equation.

To plot the phasor representation, you can use the real and imaginary axes to represent the real and imaginary parts of the complex number. The magnitude of the phasor can be represented by the length of the vector from the origin to the point on the complex plane, and the phase can be represented by the angle between the vector and the real axis.

In this case, the magnitude of the phasor is 2 and the phase is -\frac{\pi}{4}x. So for each value of x from 0 to 8, you can plot a point on the complex plane with a length of 2 and an angle of -\frac{\pi}{4}x. This will give you a series of points that, when connected, will form a phasor diagram.

Additionally, you can use the phasor representation to solve the larger engineering problem. By converting the original function into its phasor representation, you can easily manipulate and analyze the function using complex numbers and trigonometric identities. This can help you find solutions and insights that may not have been apparent from the original function.

In summary, understanding the concept of phasors and their relationship to the original function is key to plotting and using phasor representations in engineering problems. I would suggest reviewing the fundamentals of complex numbers and trigonometry to fully understand and utilize phasor representations.