Superposition of cosine functions for tides

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Homework Help Overview

The discussion revolves around the superposition of cosine functions to model tidal data more accurately. The original poster presents a specific function representing tidal data and seeks guidance on identifying an additional function to superimpose, potentially related to lunar influences.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for a second cosine function to achieve a more accurate representation of tidal data. Questions are raised about the nature of the additional function and its relation to lunar cycles. There is also confusion regarding the original poster's explanation of their function and its components.

Discussion Status

The conversation is ongoing, with participants seeking clarification and additional information. Some guidance has been offered regarding the structure of the function, but there is no clear consensus on what the second function should be or how it should be derived.

Contextual Notes

Participants note the importance of the lunar orbit and its potential effects on tides, but there is uncertainty about how to incorporate this into the mathematical model. The original poster's request for help indicates a lack of clarity on the necessary components for the superimposed function.

flyinghigh
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Homework Statement


I have 1.805cos(2pi / 12.165x) +3.125 as the function of tidal data. However I need to use another function, superimpose, to more accurately graph the data for the tides. And yeah I'm pretty lost... Does the next function have to be something to do wit the moon and its rotation around earth?

And help would be greatly appreciated :)
 
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I have no idea what you are asking! Why is that not accurate? What do you mean by "superimpose" another function?
 
Sorry, should of explained that to find a more accurate representation of the tide, you use the sum of two cosine functions, which is also known as superposition. So yeah, the tide is represented by y1+y2, where y1=the above function, y2=??...
 
that obviously depends upon the data!
 
Well then what area of the data? Since I already have the first function that takes into account the tide heights and occurrence, what else is required? That's why I asked if it was based on the moon's orbit etc.
 
Anyone have any advice?
 
flyinghigh said:
I have 1.805cos(2pi / 12.165x) +3.125 as the function of tidal data. However I need to use another function, superimpose, to more accurately graph the data for the tides. And yeah I'm pretty lost... Does the next function have to be something to do wit the moon and its rotation around earth?
You have to be more explicit. What does that mean? What is x? What are you trying to show?
 
Defennder said:
You have to be more explicit. What does that mean? What is x? What are you trying to show?

1.805 is the amplitude of the waves, as in the average difference between the high tide and the low tide. 2pi/12.165x is the period of the tide, as in how frequently it occurs. 3.125 is the average water height and hence the vertical phase shift of the function. So then I need another function in the same form, as in y=Acos(Bx-C)+D, that I then add to my function.

I'm trying to show, more accurately, tidal data. I think the second function has to be something to do with the moon and it's effects on certain tides? But yeah anyone who know's what they're talking about please help!

Thanks

flyinghigh
 

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