freqEq1Error(0)
ans =
0
freqEq1Error(1)
ans =
2.5574
freqEq1Error(2)
ans =
-0.1850
freqEq1Error(1.9)
ans =
-1.0271
freqEq1Error(2.1)
ans =
0.3902
omegaVals=[0:10]
omegaVals =
Columns 1 through 8
0 1 2 3 4 5 6 7
Columns 9 through 11
8 9 10
omegaVals=[0:0.05:10]
omegaVals =
Columns 1 through 5
0 0.0500 0.1000 0.1500 0.2000
Columns 6 through 10
0.2500 0.3000 0.3500 0.4000 0.4500
Columns 11 through 15
0.5000 0.5500 0.6000 0.6500 0.7000
Columns 16 through 20
0.7500 0.8000 0.8500 0.9000 0.9500
Columns 21 through 25
1.0000 1.0500 1.1000 1.1500 1.2000
Columns 26 through 30
1.2500 1.3000 1.3500 1.4000 1.4500
Columns 31 through 35
1.5000 1.5500 1.6000 1.6500 1.7000
Columns 36 through 40
1.7500 1.8000 1.8500 1.9000 1.9500
Columns 41 through 45
2.0000 2.0500 2.1000 2.1500 2.2000
Columns 46 through 50
2.2500 2.3000 2.3500 2.4000 2.4500
Columns 51 through 55
2.5000 2.5500 2.6000 2.6500 2.7000
Columns 56 through 60
2.7500 2.8000 2.8500 2.9000 2.9500
Columns 61 through 65
3.0000 3.0500 3.1000 3.1500 3.2000
Columns 66 through 70
3.2500 3.3000 3.3500 3.4000 3.4500
Columns 71 through 75
3.5000 3.5500 3.6000 3.6500 3.7000
Columns 76 through 80
3.7500 3.8000 3.8500 3.9000 3.9500
Columns 81 through 85
4.0000 4.0500 4.1000 4.1500 4.2000
Columns 86 through 90
4.2500 4.3000 4.3500 4.4000 4.4500
Columns 91 through 95
4.5000 4.5500 4.6000 4.6500 4.7000
Columns 96 through 100
4.7500 4.8000 4.8500 4.9000 4.9500
Columns 101 through 105
5.0000 5.0500 5.1000 5.1500 5.2000
Columns 106 through 110
5.2500 5.3000 5.3500 5.4000 5.4500
Columns 111 through 115
5.5000 5.5500 5.6000 5.6500 5.7000
Columns 116 through 120
5.7500 5.8000 5.8500 5.9000 5.9500
Columns 121 through 125
6.0000 6.0500 6.1000 6.1500 6.2000
Columns 126 through 130
6.2500 6.3000 6.3500 6.4000 6.4500
Columns 131 through 135
6.5000 6.5500 6.6000 6.6500 6.7000
Columns 136 through 140
6.7500 6.8000 6.8500 6.9000 6.9500
Columns 141 through 145
7.0000 7.0500 7.1000 7.1500 7.2000
Columns 146 through 150
7.2500 7.3000 7.3500 7.4000 7.4500
Columns 151 through 155
7.5000 7.5500 7.6000 7.6500 7.7000
Columns 156 through 160
7.7500 7.8000 7.8500 7.9000 7.9500
Columns 161 through 165
8.0000 8.0500 8.1000 8.1500 8.2000
Columns 166 through 170
8.2500 8.3000 8.3500 8.4000 8.4500
Columns 171 through 175
8.5000 8.5500 8.6000 8.6500 8.7000
Columns 176 through 180
8.7500 8.8000 8.8500 8.9000 8.9500
Columns 181 through 185
9.0000 9.0500 9.1000 9.1500 9.2000
Columns 186 through 190
9.2500 9.3000 9.3500 9.4000 9.4500
Columns 191 through 195
9.5000 9.5500 9.6000 9.6500 9.7000
Columns 196 through 200
9.7500 9.8000 9.8500 9.9000 9.9500
Column 201
10.0000
errorVals=freqEq1Error(omegaVals)
errorVals =
Columns 1 through 5
0 0.1000 0.2003 0.3011 0.4027
Columns 6 through 10
0.5053 0.6093 0.7150 0.8228 0.9331
Columns 11 through 15
1.0463 1.1631 1.2841 1.4102 1.5423
Columns 16 through 20
1.6816 1.8296 1.9883 2.1602 2.3484
Columns 21 through 25
2.5574 2.7933 3.0648 3.3845 3.7722
Columns 26 through 30
4.2596 4.9021 5.8052 7.1979 9.6881
Columns 31 through 35
15.6014 49.6285 -32.6325 -10.9493 -5.9966
Columns 36 through 40
-3.7704 -2.4863 -1.6381 -1.0271 -0.5595
Columns 41 through 45
-0.1850 0.1254 0.3902 0.6210 0.8262
Columns 46 through 50
1.0114 1.1808 1.3375 1.4840 1.6220
Columns 51 through 55
1.7530 1.8781 1.9984 2.1146 2.2273
Columns 56 through 60
2.3371 2.4445 2.5499 2.6536 2.7560
Columns 61 through 65
2.8575 2.9582 3.0584 3.1584 3.2585
Columns 66 through 70
3.3588 3.4597 3.5615 3.6643 3.7686
Columns 71 through 75
3.8746 3.9827 4.0935 4.2073 4.3247
Columns 76 through 80
4.4466 4.5736 4.7068 4.8474 4.9971
Columns 81 through 85
5.1578 5.3321 5.5235 5.7366 5.9778
Columns 86 through 90
6.2563 6.5858 6.9876 7.4963 8.1733
Columns 91 through 95
9.1373 10.6538 13.4602 20.6577 85.4128
Columns 96 through 100
-21.8254 -6.5849 -2.3709 -0.3675 0.8209
Columns 101 through 105
1.6195 2.2014 2.6506 3.0126 3.3144
Columns 106 through 110
3.5727 3.7987 4.0002 4.1825 4.3495
Columns 111 through 115
4.5044 4.6493 4.7861 4.9160 5.0403
Columns 116 through 120
5.1598 5.2753 5.3875 5.4969 5.6039
Columns 121 through 125
5.7090 5.8125 5.9147 6.0160 6.1166
Columns 126 through 130
6.2168 6.3168 6.4169 6.5173 6.6184
Columns 131 through 135
6.7203 6.8233 6.9279 7.0342 7.1428
Columns 136 through 140
7.2540 7.3683 7.4865 7.6091 7.7371
Columns 141 through 145
7.8714 8.0135 8.1649 8.3277 8.5046
Columns 146 through 150
8.6993 8.9166 9.1633 9.4493 9.7892
Columns 151 through 155
10.2060 10.7377 11.4523 12.4842 14.1429
Columns 156 through 160
17.3324 26.3068 259.0018 -13.8151 -2.4326
Columns 161 through 165
1.2003 3.0139 4.1176 4.8711 5.4263
Columns 166 through 170
5.8583 6.2086 6.5021 6.7543 6.9757
Columns 171 through 175
7.1736 7.3531 7.5180 7.6710 7.8144
Columns 176 through 180
7.9499 8.0789 8.2023 8.3211 8.4360
Columns 181 through 185
8.5477 8.6566 8.7633 8.8681 8.9714
Columns 186 through 190
9.0734 9.1746 9.2751 9.3752 9.4752
Columns 191 through 195
9.5754 9.6759 9.7770 9.8791 9.9824
Columns 196 through 200
10.0872 10.1939 10.3029 10.4146 10.5295
Column 201
10.6484
errorVals=freqEq1Error(omegaVals);
plot(omegaVals',errorVals')
help plot
plot Linear plot.
plot(X,Y) plots vector Y versus vector X. If X or Y is a matrix,
then the vector is plotted versus the rows or columns of the matrix,
whichever line up. If X is a scalar and Y is a vector, disconnected
line objects are created and plotted as discrete points vertically at
X.
plot(Y) plots the columns of Y versus their index.
If Y is complex, plot(Y) is equivalent to plot(real(Y),imag(Y)).
In all other uses of plot, the imaginary part is ignored.
Various line types, plot symbols and colors may be obtained with
plot(X,Y,S) where S is a character string made from one element
from any or all the following 3 columns:
b blue . point - solid
g green o circle : dotted
r red x x-mark -. dashdot
c cyan + plus -- dashed
m magenta * star (none) no line
y yellow s square
k black d diamond
w white v triangle (down)
^ triangle (up)
< triangle (left)
> triangle (right)
p pentagram
h hexagram
For example, plot(X,Y,'c+:') plots a cyan dotted line with a plus
at each data point; plot(X,Y,'bd') plots blue diamond at each data
point but does not draw any line.
plot(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...) combines the plots defined by
the (X,Y,S) triples, where the X's and Y's are vectors or matrices
and the S's are strings.
For example, plot(X,Y,'y-',X,Y,'go') plots the data twice, with a
solid yellow line interpolating green circles at the data points.
The plot command, if no color is specified, makes automatic use of
the colors specified by the axes ColorOrder property. By default,
plot cycles through the colors in the ColorOrder property. For
monochrome systems, plot cycles over the axes LineStyleOrder property.
Note that RGB colors in the ColorOrder property may differ from
similarly-named colors in the (X,Y,S) triples. For example, the
second axes ColorOrder property is medium green with RGB [0 .5 0],
while plot(X,Y,'g') plots a green line with RGB [0 1 0].
If you do not specify a marker type, plot uses no marker.
If you do not specify a line style, plot uses a solid line.
plot(AX,...) plots into the axes with handle AX.
plot returns a column vector of handles to lineseries objects, one
handle per plotted line.
The X,Y pairs, or X,Y,S triples, can be followed by
parameter/value pairs to specify additional properties
of the lines. For example, plot(X,Y,'LineWidth',2,'Color',[.6 0 0])
will create a plot with a dark red line width of 2 points.
Example
x = -pi:pi/10:pi;
y = tan(sin(x)) - sin(tan(x));
plot(x,y,'--rs','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g',...
'MarkerSize',10)
See also plottools, semilogx, semilogy, loglog, plotyy, plot3, grid,
title, xlabel, ylabel, axis, axes, hold, legend, subplot, scatter.
Reference page for plot
Other functions named plot
plot(omegaVals',errorVals','--or','LineWidth',2)
plot(omegaVals',errorVals')
axis([0 10 -10 10])
grid on
set(gca)
ALim: {}
ALimMode: {'auto' 'manual'}
ActivePositionProperty: {1×2 cell}
AmbientLightColor: {1×0 cell}
Box: {'on' 'off'}
BoxStyle: {'full' 'back'}
BusyAction: {'queue' 'cancel'}
ButtonDownFcn: {}
CLim: {}
CLimMode: {'auto' 'manual'}
CameraPosition: {}
CameraPositionMode: {'auto' 'manual'}
CameraTarget: {}
CameraTargetMode: {'auto' 'manual'}
CameraUpVector: {}
CameraUpVectorMode: {'auto' 'manual'}
CameraViewAngle: {}
CameraViewAngleMode: {'auto' 'manual'}
Children: {}
Clipping: {'on' 'off'}
ClippingStyle: {1×2 cell}
Color: {1×0 cell}
ColorOrder: {}
ColorOrderIndex: {}
CreateFcn: {}
DataAspectRatio: {}
DataAspectRatioMode: {'auto' 'manual'}
DeleteFcn: {}
FontAngle: {'normal' 'italic'}
FontName: {}
FontSize: {}
FontSmoothing: {'on' 'off'}
FontUnits: {1×5 cell}
FontWeight: {'normal' 'bold'}
GridAlpha: {}
GridAlphaMode: {'auto' 'manual'}
GridColor: {1×0 cell}
GridColorMode: {'auto' 'manual'}
GridLineStyle: {1×5 cell}
HandleVisibility: {1×3 cell}
HitTest: {'on' 'off'}
Interruptible: {'on' 'off'}
LabelFontSizeMultiplier: {}
Layer: {'bottom' 'top'}
LineStyleOrder: {}
LineStyleOrderIndex: {}
LineWidth: {}
MinorGridAlpha: {}
MinorGridAlphaMode: {'auto' 'manual'}
MinorGridColor: {1×0 cell}
MinorGridColorMode: {'auto' 'manual'}
MinorGridLineStyle: {1×5 cell}
NextPlot: {1×4 cell}
OuterPosition: {}
Parent: {}
PickableParts: {1×3 cell}
PlotBoxAspectRatio: {}
PlotBoxAspectRatioMode: {'auto' 'manual'}
Position: {}
Projection: {1×2 cell}
Selected: {'on' 'off'}
SelectionHighlight: {'on' 'off'}
SortMethod: {1×2 cell}
Tag: {}
TickDir: {'in' 'out' 'both'}
TickDirMode: {'auto' 'manual'}
TickLabelInterpreter: {1×3 cell}
TickLength: {}
Title: {}
TitleFontSizeMultiplier: {}
TitleFontWeight: {'normal' 'bold'}
UIContextMenu: {}
Units: {1×6 cell}
UserData: {}
View: {}
Visible: {'on' 'off'}
XAxis: {}
XAxisLocation: {1×3 cell}
XColor: {1×0 cell}
XColorMode: {'auto' 'manual'}
XDir: {'normal' 'reverse'}
XGrid: {'on' 'off'}
XLabel: {}
XLim: {}
XLimMode: {'auto' 'manual'}
XMinorGrid: {'on' 'off'}
XMinorTick: {'on' 'off'}
XScale: {'linear' 'log'}
XTick: {}
XTickLabel: {}
XTickLabelMode: {'auto' 'manual'}
XTickLabelRotation: {}
XTickMode: {'auto' 'manual'}
YAxisLocation: {1×3 cell}
YColor: {1×0 cell}
YColorMode: {'auto' 'manual'}
YDir: {'normal' 'reverse'}
YGrid: {'on' 'off'}
YLabel: {}
YLim: {}
YLimMode: {'auto' 'manual'}
YMinorGrid: {'on' 'off'}
YMinorTick: {'on' 'off'}
YScale: {'linear' 'log'}
YTick: {}
YTickLabel: {}
YTickLabelMode: {'auto' 'manual'}
YTickLabelRotation: {}
YTickMode: {'auto' 'manual'}
ZAxis: {}
ZColor: {1×0 cell}
ZColorMode: {'auto' 'manual'}
ZDir: {'normal' 'reverse'}
ZGrid: {'on' 'off'}
ZLabel: {}
ZLim: {}
ZLimMode: {'auto' 'manual'}
ZMinorGrid: {'on' 'off'}
ZMinorTick: {'on' 'off'}
ZScale: {'linear' 'log'}
ZTick: {}
ZTickLabel: {}
ZTickLabelMode: {'auto' 'manual'}
ZTickLabelRotation: {}
ZTickMode: {'auto' 'manual'}
set(gca,'xaxislocation','origin')
xlabel('omega')
ylabel('error (k=1)')
title("Frequency Equation Error (k=1)')
title("Frequency Equation Error (k=1)')
{Error: String is not terminated properly.
}
title('Frequency Equation Error (k=1)')
help fzero
fzero Single-variable nonlinear zero finding.
X = fzero(FUN,X0) tries to find a zero of the function FUN near X0,
if X0 is a scalar. It first finds an interval containing X0 where the
function values of the interval endpoints differ in sign, then searches
that interval for a zero. FUN is a function handle. FUN accepts real
scalar input X and returns a real scalar function value F, evaluated
at X. The value X returned by fzero is near a point where FUN changes
sign (if FUN is continuous), or NaN if the search fails.
X = fzero(FUN,X0), where X0 is a vector of length 2, assumes X0 is a
finite interval where the sign of FUN(X0(1)) differs from the sign of
FUN(X0(2)). An error occurs if this is not true. Calling fzero with a
finite interval guarantees fzero will return a value near a point where
FUN changes sign.
X = fzero(FUN,X0), where X0 is a scalar value, uses X0 as a starting
guess. fzero looks for an interval containing a sign change for FUN and
containing X0. If no such interval is found, NaN is returned.
In this case, the search terminates when the search interval
is expanded until an Inf, NaN, or complex value is found. Note: if
the option FunValCheck is 'on', then an error will occur if an NaN or
complex value is found.
X = fzero(FUN,X0,OPTIONS) solves the equation with the default optimization
parameters replaced by values in the structure OPTIONS, an argument
created with the OPTIMSET function. See OPTIMSET for details. Used
options are Display, TolX, FunValCheck, OutputFcn, and PlotFcns.
X = fzero(PROBLEM) finds the zero of a function defined in PROBLEM.
PROBLEM is a structure with the function FUN in PROBLEM.objective,
the start point in PROBLEM.x0, the options structure in PROBLEM.options,
and solver name 'fzero' in PROBLEM.solver.
[X,FVAL]= fzero(FUN,...) returns the value of the function described
in FUN, at X.
[X,FVAL,EXITFLAG] = fzero(...) returns an EXITFLAG that describes the
exit condition. Possible values of EXITFLAG and the corresponding exit
conditions are
1 fzero found a zero X.
-1 Algorithm terminated by output function.
-3 NaN or Inf function value encountered during search for an interval
containing a sign change.
-4 Complex function value encountered during search for an interval
containing a sign change.
-5 fzero may have converged to a singular point.
-6 fzero can not detect a change in sign of the function.
[X,FVAL,EXITFLAG,OUTPUT] = fzero(...) returns a structure OUTPUT
with the number of function evaluations in OUTPUT.funcCount, the
algorithm name in OUTPUT.algorithm, the number of iterations to
find an interval (if needed) in OUTPUT.intervaliterations, the
number of zero-finding iterations in OUTPUT.iterations, and the
exit message in OUTPUT.message.
Examples
FUN can be specified using @:
X = fzero(@sin,3)
returns pi.
X = fzero(@sin,3,optimset('Display','iter'))
returns pi, uses the default tolerance and displays iteration information.
FUN can be an anonymous function:
X = fzero(@(x) sin(3*x),2)
FUN can be a parameterized function. Use an anonymous function to
capture the problem-dependent parameters:
myfun = @(x,c) cos(c*x); % The parameterized function.
c = 2; % The parameter.
X = fzero(@(x) myfun(x,c),0.1)
Limitations
X = fzero(@(x) abs(x)+1, 1)
returns NaN since this function does not change sign anywhere on the
real axis (and does not have a zero as well).
X = fzero(@tan,2)
returns X near 1.5708 because the discontinuity of this function near the
point X gives the appearance (numerically) that the function changes sign at X.
See also roots, fminbnd, function_handle.
Reference page for fzero
omega1=fzero('freqEq1Error',2)
omega1 =
2.0288
omega1=fzero('freqEq1Error',0.5*pi)
omega1 =
1.5708
omega1=fzero('freqEq1Error',[2 2.1])
omega1 =
2.0288
errorVals=freqEq1Error(omegaVals)
errorVals =
Columns 1 through 5
0 0.0999 0.1993 0.2978 0.3947
Columns 6 through 10
0.4896 0.5821 0.6717 0.7578 0.8402
Columns 11 through 15
0.9182 0.9916 1.0598 1.1226 1.1796
Columns 16 through 20
1.2304 1.2747 1.3123 1.3428 1.3660
Columns 21 through 25
1.3818 1.3899 1.3902 1.3825 1.3669
Columns 26 through 30
1.3431 1.3113 1.2714 1.2234 1.1674
Columns 31 through 35
1.1036 1.0320 0.9529 0.8663 0.7726
Columns 36 through 40
0.6721 0.5649 0.4514 0.3320 0.2071
Columns 41 through 45
0.0770 -0.0578 -0.1970 -0.3399 -0.4862
Columns 46 through 50
-0.6353 -0.7867 -0.9399 -1.0943 -1.2493
Columns 51 through 55
-1.4044 -1.5590 -1.7124 -1.8642 -2.0136
Columns 56 through 60
-2.1602 -2.3032 -2.4422 -2.5765 -2.7056
Columns 61 through 65
-2.8289 -2.9458 -3.0557 -3.1583 -3.2529
Columns 66 through 70
-3.3391 -3.4164 -3.4844 -3.5427 -3.5908
Columns 71 through 75
-3.6284 -3.6552 -3.6709 -3.6751 -3.6678
Columns 76 through 80
-3.6487 -3.6175 -3.5743 -3.5189 -3.4513
Columns 81 through 85
-3.3714 -3.2793 -3.1751 -3.0588 -2.9307
Columns 86 through 90
-2.7909 -2.6396 -2.4772 -2.3039 -2.1201
Columns 91 through 95
-1.9261 -1.7225 -1.5096 -1.2880 -1.0581
Columns 96 through 100
-0.8207 -0.5762 -0.3252 -0.0685 0.1932
Columns 101 through 105
0.4594 0.7292 1.0019 1.2767 1.5528
Columns 106 through 110
1.8295 2.1059 2.3812 2.6546 2.9252
Columns 111 through 115
3.1921 3.4547 3.7119 3.9630 4.2072
Columns 116 through 120
4.4436 4.6714 4.8899 5.0982 5.2957
Columns 121 through 125
5.4816 5.6552 5.8158 5.9627 6.0955
Columns 126 through 130
6.2134 6.3159 6.4026 6.4729 6.5265
Columns 131 through 135
6.5629 6.5819 6.5831 6.5662 6.5312
Columns 136 through 140
6.4778 6.4060 6.3157 6.2069 6.0798
Columns 141 through 145
5.9343 5.7707 5.5893 5.3902 5.1738
Columns 146 through 150
4.9405 4.6908 4.4251 4.1440 3.8480
Columns 151 through 155
3.5378 3.2140 2.8775 2.5289 2.1691
Columns 156 through 160
1.7990 1.4194 1.0312 0.6355 0.2332
Columns 161 through 165
-0.1746 -0.5870 -1.0028 -1.4210 -1.8403
Columns 166 through 170
-2.2598 -2.6783 -3.0945 -3.5074 -3.9158
Columns 171 through 175
-4.3186 -4.7146 -5.1026 -5.4815 -5.8503
Columns 176 through 180
-6.2077 -6.5527 -6.8843 -7.2014 -7.5029
Columns 181 through 185
-7.7881 -8.0558 -8.3052 -8.5354 -8.7457
Columns 186 through 190
-8.9352 -9.1032 -9.2492 -9.3723 -9.4722
Columns 191 through 195
-9.5483 -9.6001 -9.6273 -9.6296 -9.6067
Columns 196 through 200
-9.5584 -9.4847 -9.3854 -9.2605 -9.1103
Column 201
-8.9347
plot(omegaVals',errorVals')
grid on
set(gca,'xaxislocation','origin')
xlabel('omega')
ylabel('error (k=1)')
title('Frequency Equation Error (k=1)')
errorVals=freqEq1Error(omegaVals);
omega1=fzero('freqEq1Error',[0.5*pi 1.5*pi])
omega1 =
2.0288
set(gca,'xtick',[0:pi:3*pi])
omega1=fzero('freqEq1Error',[0.5*pi 1.5*pi])
omega1 =
2.0288
omega2=fzero('freqEq1Error',[1.5*pi 2.5*pi])
omega2 =
4.9132
omega3=fzero('freqEq1Error',[2.5*pi 3.5*pi])
omega3 =
7.9787
omega4=fzero('freqEq1Error',[3.5*pi 4.5*pi])
omega4 =
11.0855
3.5*pi
ans =
10.9956
omega4Interval=[3.5*pi 4.5*pi]
omega4Interval =
10.9956 14.1372
omega4=fzero('freqEq1Error',omega4Interval)
omega4 =
11.0855
omega1=fzero(@(omega) freqEq1Error(omega,k),[0.5*pi 1.5*pi])
{Error using fzero (line 246)
FZERO cannot continue because user-supplied
function_handle ==> @(omega)freqEq1Error(omega,k)
failed with the error below.
Undefined function or variable 'k'.}
k=1
k =
1
omega1=fzero(@(omega) freqEqError(omega,k),[0.5*pi 1.5*pi])
omega1 =
2.0288
omega1=fzero(@(omega) freqEqError(omega,k),[0.5*pi 1.5*pi])
omega1 =
2.0288
fzero(@(omega) freqEqError(omega,k),[1.5*pi 2.5*pi])
ans =
4.9132
omega2=fzero(@(omega) freqEqError(omega,k),[1.5*pi 2.5*pi])
omega2 =
4.9132
k=2
k =
2
omega1=fzero(@(omega) freqEqError(omega,k),[0.5*pi 1.5*pi])
omega1 =
1.8366
fprintf('For k = %f, frequency %i equals: %f',k,1,omega1)
For k = 2.000000, frequency 1 equals: 1.836597aaa
{Undefined function or variable 'aaa'.}
fprintf('For k = %f, frequency %i equals: %f\n',k,1,omega1)
For k = 2.000000, frequency 1 equals: 1.836597
fprintf('For k = %4.2f, frequency %1i equals: %10.8f\n',k,1,omega1)
For k = 2.00, frequency 1 equals: 1.83659720