$Analyzing Concave Down Segments of the Sinusoidal Curve$

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$Analyzing Concave Down Segments of the Sinusoidal Curve$

I am working on analyzing a specific segment of the sinusoidal curve, particularly the portion that is concave down. For this segment, I have two primary measurements I would like to determine:

*The vertical curvature C from the local maximum (turning point) of the sinusoidal curve to the vertex of the parabola on Drop axis Z that best fits this segment.*
*The horizontal distance, or width, between the two points (A1 and B1) on the sinusoidal curve that are immediately before and after the vertex of this fitting parabola.*

Could someone please provide guidance on how to compute these measurements, or suggest a method or transformation that simplifies this analysis? Any help or references to relevant literature would be greatly appreciated.

Geometry Trigonometry Wave Equation

Andrius Mickevicius

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Erdos

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The offered bounty is a bit low.
- Andrius Mickevicius
  
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  It's not difficult solution i believe i upped bounty a little bit

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Erdos

0

The offered bounty is a bit low.

Andrius Mickevicius

0

It's not difficult solution i believe i upped bounty a little bit
Andrius Mickevicius

0

It's not difficult solution i believe i upped bounty a little bit

Answer 1

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Hi Andrius,

Here is a detailed approach you can use:

Get the data points details
1. Manually extract data points if you have the coordinates.
2. Digitize the chart to get coordinates, if needed.
3. For each curve, create a data set with x and y coordinates.
Define the model function
1. Use curve fitting to model/fit each section of the graph based on the extracted data points in previous step.
2. For example, you can use the following model functions in general:
  1. Sinusoidal Curve: $y=aSin⁡(bx+c)+d$
  2. Parabolic Curve: $y=ax^{2} +bx+c$
Fit the model to the data
1. Use Python or R to fit models to your data
Plot the data and the fitted curve
1. Plot the fitted curve to check visually and make sure the process worked as it should.
2. If the fitted curves don't look good, go back to Steps 1-3 and repeat.
Calculate curvature at the vertex
1. Calculate the curvature of a curve using its formulas for k
Calculate the distance between A and B
1. Calculate the distance between two points using its formula

Ideally, you can automate all these calculations in a script to make it more efficient to try different curves, etc.

If you need help with coding this, you can add a seperate direct question to me.

Best Regards,
Kav10

Kav10

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Kav10

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@Andrius, like I said the website does not allow off site interaction. If you need help with coding this, you can go to my profile, click on “Ask direct question” and create the question so I can help.

$Analyzing Concave Down Segments of the Sinusoidal Curve$

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