undefined t variable in gnuplot

Question

I am trying to plot a gaussian wave cos((0.1*x)*exp(-sqrt(x)/2*sqrt(t))) in gnuplot. I define a range for t by:

set trange [0.1:2] 
plot cos((0.1*x)*exp(-sqrt(x)/2*sqrt(t)))

but it stops with undefined variable t error. What should I do?

Answer 1

The plot command works with functions of a single variable. Thus it will fill in the x value, but when it encounters t, it doesn't know what to do with that.

If you had previously defined t, it would use that value. Thus

t = 0.5
plot cos((0.1*x)*exp(-sqrt(x)/2*sqrt(t)))

will work just fine, using a value of 0.5 for t.

If you wish to plot multiple curves for a range of t values, you can use the plot for syntax doing something like

plot for [t=0:10] cos((0.1*x)*exp(-sqrt(x)/2*sqrt(0.1+t*0.19)))

which will plot the curve for a range of values. As the for syntax works with integers, we need to use an integer value for the loop and then calculate the value for the formula (0.1+t*0.19 ranges from 0.1 to 2 as required when t ranges from 0 to 10). You can label the key using

plot for [t=0:10] cos((0.1*x)*exp(-sqrt(x)/2*sqrt(0.1+t*0.19))) title sprintf("t=%f",0.1+t*0.19)

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Setting a range will only work with variables that the plot command understands. As t isn't one of them (except in parametric mode), the range command doesn't do anything in this case.