Problem with FindFit

1. May 13, 2012

Hoiya

I have these values:

Oscill = {{0, -6.4}, {5, -6.3}, {10, -6.5}, {15, -6.2}, {20, -6.1}, \
{25, -5.9}, {30, -5.8}, {35, -5.5}, {40, -5.1}, {45, -4.8}, {50, \
-4.4}, {55, -3.9}, {60, -3.3}, {65, -2.8}, {70, -2.2}, {75, -1.8}, \
{80, -1}, {85, -0.4}, {90, 0.4}, {95, 1}, {100, 1.8}, {105,
2.3}, {110, 3}, {115, 3.8}, {120, 4.9}, {140, 8}, {160,
11.1}, {180, 13.8}, {200, 16.3}, {220, 18.2}, {240, 19.7}, {260,
20.4}, {280, 20.4}, {300, 19.8}, {320, 18.7}, {340, 17}, {360,
15}, {380, 12.7}, {400, 10.3}, {420, 7.8}, {440, 5.5}, {460,
3.6}, {480, 1.8}, {500, 0.6}, {520, -0.2}, {540, -0.3}, {560,
0}, {580, 0.8}, {600, 1.9}, {620, 3.5}, {640, 5.2}, {660,
7.1}, {680, 8.9}, {700, 10.8}, {720, 12.4}, {740, 13.8}, {760,
14.7}, {780, 15.5}, {800, 15.8}, {820, 15.6}, {840, 15.1}, {860,
14.3}, {880, 13.1}, {900, 11.8}, {920, 10.4}, {940, 8.9}, {960,
7.5}, {980, 6.1}, {1000, 5}, {1020, 4.2}, {1040, 3.6}, {1060,
3.2}, {1080, 3.3}, {1100, 3.6}, {1120, 4.1}, {1140, 4.9}, {1160,
5.8}, {1180, 7}, {1200, 8.1}, {1220, 9.2}, {1240, 10.3}, {1260,
11.2}, {1280, 11.9}, {1300, 12.4}, {1320, 12.8}, {1340,
12.8}, {1360, 12.7}, {1380, 12.3}, {1400, 11.7}, {1420, 11}, {1440,
10.1}, {1460, 9.3}, {1480, 8.4}, {1500, 7.6}, {1520, 6.8}, {1540,
6.3}, {1560, 5.7}, {1580, 5.4}, {1600, 5.3}, {1620, 5.4}, {1640,
5.7}, {1660, 6}, {1680, 6.4}, {1700, 7}, {1720, 7.8}, {1740,
8.4}, {1760, 9}, {1780, 9.6}, {1800, 10.1}, {1820, 10.6}, {1840,
10.8}, {1860, 10.9}, {1880, 10.9}, {1900, 10.8}, {1920,
10.6}, {1940, 10.1}, {1960, 9.7}, {1980, 9.2}, {2000, 8.7}, {2020,
8.1}, {2040, 7.7}, {2060, 7.1}, {2080, 6.9}, {2100, 6.6}, {2120,
6.5}, {2140, 6.5}, {2160, 6.5}, {2180, 6.7}, {2200, 7}, {2220,
7.2}, {2240, 7.7}, {2260, 8.1}, {2280, 8.4}, {2300, 8.9}, {2320,
9.1}, {2340, 9.5}, {2360, 9.7}, {2380, 9.8}, {2400, 9.9}, {2420,
9.8}, {2440, 9.8}, {2460, 9.7}, {2480, 9.3}, {2500, 9.1}, {2520,
8.8}, {2540, 8.6}, {2560, 8.2}, {2580, 8}, {2600, 7.7}, {2620,
7.5}, {2640, 7.4}, {2660, 7.3}, {2680, 7.4}, {2700, 7.4}, {2720,
7.5}, {2740, 7.6}, {2760, 7.8}, {2780, 8}, {2800, 8.2}, {2820,
8.5}, {2840, 8.7}, {2860, 8.9}, {2880, 9}, {2900, 9.1}, {2920,
9.2}, {2940, 9.3}, {2960, 9.3}, {2980, 9.2}, {3000, 9.1}, {3020,
9}, {3040, 8.9}, {3060, 8.7}, {3080, 8.5}, {3100, 8.3}, {3120,
8.1}, {3140, 8}, {3160, 7.9}, {3180, 7.8}, {3200, 7.7}, {3220,
7.7}, {3240, 7.8}, {3260, 7.8}, {3280, 7.9}, {3300, 8.0}, {3320,
8.1}, {3340, 8.3}, {3360, 8.4}, {3380, 8.5}, {3400, 8.6}, {3420,
8.7}, {3440, 8.8}, {3460, 8.8}, {3480, 8.9}, {3500, 8.9}, {3520,
8.8}, {3540, 8.8}, {3560, 8.7}, {3580, 8.6}, {3600, 8.5}}

and this function:

Espo = A*(e^(-\[Sigma]*t))*Cos[((2*Pi/T)*t) + \[Theta]] + \[Phi]

When I try to use findfit, I read this error message:

FEO = FindFit[Oscill, Espo, {A, \[Sigma], T, \[Theta], \[Phi]}, t]

FindFit::nrlnum: The function value {7.9403,7.3+0.540302/e^5.,7.5+0.540302/e^10.,7.2+0.540302/e^15.,7.1+<<19>>/e^<<4>>,<<1>>,6.8+<<1>>,6.5+0.540302/e^35.,6.1+0.540302/e^40.,5.8+0.540302/e^45.,<<189>>} is not a list of real numbers with dimensions {199} at {A,\[Sigma],T,\[Theta],\[Phi]} = {1.,1.,1.,1.,1.}. >>

FindFit::nrlnum: The function value {7.9403,7.3+0.540302/e^5.,7.5+0.540302/e^10.,7.2+0.540302/e^15.,7.1+<<19>>/e^<<4>>,<<1>>,6.8+<<1>>,6.5+0.540302/e^35.,6.1+0.540302/e^40.,5.8+0.540302/e^45.,<<189>>} is not a list of real numbers with dimensions {199} at {A,\[Sigma],T,\[Theta],\[Phi]} = {1.,1.,1.,1.,1.}. >>

Can anybody help me?

2. May 13, 2012

Bill Simpson

Replace this
Espo = A*(e^...
with this
Espo = A*(E^...