Phase shift and sinusoidal curve fitting - Finding .

In summary, To find the period and amplitude of the function y = 4sin(2x - pi), we use the formula Period = 2pi/|b| and Amplitude = |a|, where a and b are the coefficients of sin(ax + b). In this case, the period is 2 and the amplitude is 4. The phase shift can be found using the formula phi = b/a, so in this case it is pi/2. To graph the function, plot points in steps of 0.1 radians for x from 0 to 2pi, then complete the plot back to -pi. This will help in identifying the key points of the function."
  • #1
nukeman
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Phase shift and sinusoidal curve fitting - Finding...

Homework Statement



"Find the period, amplitude, and phase shift of each function. Graph each function. Be sure to label key points"

y = 4sin(2x - pi)


Homework Equations





The Attempt at a Solution



So, I got...

Amplitude = 4
Period = 2pi/2 = 2

Phase shift: Would that be pheta/w ?, So pi/2 ?

Now here is where I get messed up.

I do not know how to get "Interval defining one cycle" and "Subinterval width"

How do I generate points from this?
 
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  • #2


First step: Graph paper. Sharp pencil. Eraser. Calculator. Plot points in steps of, say 0.1 radian, for x from 0 to 2Pi radians, plotting y vs. x

Then, complete the plot from 0 back to -Pi radians.

Do this neatly & well, and you'll discover a lot.
 
Last edited:

1. What is a phase shift in sinusoidal curve fitting?

A phase shift in sinusoidal curve fitting refers to the horizontal displacement of a sinusoidal curve on a graph. It can also be thought of as a delay or advancement of the curve relative to its original position.

2. How is the phase shift calculated in sinusoidal curve fitting?

The phase shift is calculated by finding the horizontal distance between the starting point of the curve and the point where the curve starts to repeat itself. This distance is then divided by the period of the curve to determine the phase shift value.

3. Can a phase shift be negative in sinusoidal curve fitting?

Yes, a phase shift can be negative in sinusoidal curve fitting. This indicates that the curve has shifted to the left on the graph.

4. How does phase shift affect the shape of a sinusoidal curve?

A phase shift can change the shape of a sinusoidal curve by moving the curve left or right on the graph. This can result in a compressed or stretched curve, depending on the direction and magnitude of the phase shift.

5. What is the significance of phase shift in real-world applications?

Phase shift is significant in many real-world applications, such as in signal processing and electrical engineering. It can also be used in areas such as physics and astronomy to analyze waveforms and predict the behavior of systems.

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