# Question:phaseportait. 2 different resultats with plot and with phaseportrait.

## Question:phaseportait. 2 different resultats with plot and with phaseportrait.

Hi,

I found the plotted phase portrait strange and i verified it with phaseportrait

With plot :

no respect of initial conditions

And with phase portrait :

﻿

My code is :(a=0 for no damping)

restart; Q := 1/2; omega0 := 1.8*Pi; a := 0; eqd := diff(y(t), `\$`(t, 2))+a*omega0*(diff(y(t), t))/Q+omega0^2*y(t) = cos(2*Pi*t); eqd;

sol := dsolve({eqd, y(0) = .5, (D(y))(0) = 0}, y(t));

plot([eval(y(t), sol)], t = 0 .. 10*Pi, numpoints = 2^10, tickmarks = [spacing(2*Pi), default]);

plot(eval([diff(y(t), t), y(t), t = 0 .. 50], sol), numpoints = 2^11, frames = 50);

eqd := {diff(z(t), t)+a*omega0*z(t)/Q+y(t) = cos(2*Pi*t), diff(y(t), t) = z(t)}; eqd;

DEtools[phaseportrait](eqd, [z(t), y(t)], t = 0 .. 3, [[y(0) = .5, z(0) = 0]], scene = [y(t), z(t)], stepsize = .1, linecolor = black, thickness = 2);

is that not strange ?

Moreover, i see that even this second phase portrait is not good, since when i put omega0=1.999, i obtain :

﻿So, there, amplitude is not respected in 2nd phase portrait