Where to Plot [Int |sin3t *cost3t|dt ] / [ Int (sin^2(3t)) dt]
in [Math]
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From: Bret Cahill on 19 Jul 2010 12:26 Does this look familiar? Wolfram Alpha won't plot it. An alternate form: [ (3 integral |(e^(-3 i t)-e^(3 i t)) (e^(-3 i t)+e^(3 i t))| dt) ] / (6 t-sin(6 t)) Bret Cahill
From: Ray Vickson on 19 Jul 2010 14:15 On Jul 19, 9:26 am, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > Does this look familiar? > > Wolfram Alpha won't plot it. > > An alternate form: > > [ (3 integral |(e^(-3 i t)-e^(3 i t)) (e^(-3 i t)+e^(3 i t))| > dt) ] / (6 t-sin(6 t)) > > Bret Cahill If you really mean F = int(f dt)/(6t - sin(6t)) with f = |(e^(-3 i t)- e^(3 i t)) (e^(-3 i t)+e^(3 i t))|, then I get, using Maple 9.5: F := -2*signum(sin(3*t)*cos(3*t))*cos(3*t)^2/(6*t-sin(6*t)). [signum(x) = sign(x) = x/|x| if x <>0, and in my setting, signum(0) = 0.] The plot of F looks somewhat like a damped triangular waveform, but with slightly curved "hypontenuse". R.G. Vickson
From: Bret Cahill on 20 Jul 2010 02:58 > > Does this look familiar? > > > Wolfram Alpha won't plot it. > > > An alternate form: > > > [ (3 integral |(e^(-3 i t)-e^(3 i t)) (e^(-3 i t)+e^(3 i t))| > > dt) ] / (6 t-sin(6 t)) > > > Bret Cahill > > If you really mean F = int(f dt)/(6t - sin(6t)) with f = |(e^(-3 i t)- > e^(3 i t)) (e^(-3 i t)+e^(3 i t))|, then I get, using Maple 9.5: > F := -2*signum(sin(3*t)*cos(3*t))*cos(3*t)^2/(6*t-sin(6*t)). > [signum(x) = sign(x) = x/|x| if x <>0, and in my setting, signum(0) = > 0.] The plot of F looks somewhat like a damped triangular waveform, > but with slightly curved "hypontenuse". Thanks. Is this something that shows up in science or engineering very often? Bret Cahill
From: Bret Cahill on 20 Jul 2010 12:28
> > Does this look familiar? > > > Wolfram Alpha won't plot it. > > > An alternate form: > > > [ (3 integral |(e^(-3 i t)-e^(3 i t)) (e^(-3 i t)+e^(3 i t))| > > dt) ] / (6 t-sin(6 t)) > > > Bret Cahill > > If you really mean F = int(f dt)/(6t - sin(6t)) with f = |(e^(-3 i t)- > e^(3 i t)) (e^(-3 i t)+e^(3 i t))|, then I get, using Maple 9.5: > F := -2*signum(sin(3*t)*cos(3*t))*cos(3*t)^2/(6*t-sin(6*t)). > [signum(x) = sign(x) = x/|x| if x <>0, and in my setting, signum(0) = > 0.] The plot of F looks somewhat like a damped triangular waveform, > but with slightly curved "hypontenuse". It is always positive and, except for the waves, basically horizontal? Bret Cahill |