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See Don's piece on sine curve fitting in last week's E-Bulletin.

31 August 2001

Fitting Logarithmic Curves

Don Sieber

Log Curve Fit for Increasing Values of e

E0 ;= 3 E1 ;=5 E2 ;= 6

Use symbolic to solve for tc

 

Log Curve Fit for Decreasing Values of e

Use symbolic to solve for tc

 

From this it can be seen that whether the curve is increasing or decreasing, the solution for (tc) is the same.

Find symbolic solution for Emax for ascending case:

Solution for Emax for ascending case, no solution for V.

No solution for Emax for descending case, however, V has a solution.

The solutions for Emax and V are the same and represent the limiting value of E after t approaches >5 time constants.

By symmetry, we may solve for both V and Emax because one possible solution is where E₀ - V = Emax - E₀. So 2E₀ = Emax - V. This in turn allows us to solve for T. There are 3 conditions:

1. E₀ grows toward E₂ and Emax.
2. E₀ decreases toward E₂ and V.
3. E₁ is greater or less than E₀ and E₂ in which case there is no solution and a sine curve fit program may be used.