Plot a quartic expression with two variables?

Questions
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1

Hi guys, new user here…trying to figure out what I’m missing here

The idea is to get a graph similar to this one

campbell.PNG
campbell.PNG552×387 40.1 KB

m = 10;
Jp = 2;
Jt = 1.2;
l = 0.2;
k12 = 0;
ka = 2.5*(10^6);
k11 = 2*ka;
k22 = (0.5^2 + 0.5^2)*ka;
Eqt = \[Omega]^4 - \[Omega]^3*\[CapitalOmega]*(Jp/
      Jt) - \[Omega]^2 ((k11/m) + (k22/
        Jt)) + \[Omega]*\[CapitalOmega]*((k11*Jp)/(m*Jt)) + ((k11*
        k22 - k12^2)/(m*Jt)) == 0
Plot[Eqt, {\[Omega], -1000, 1500}, {\[CapitalOmega], 0, 1500}]

The Eqt term is the quartic equation and there is two variables ? and ? (abscissae). I could only plot3d it… any suggestions to plot like the graph above.

cheers,

2

I think you need to solve Eqt

3

You can use ContourPlot:

ContourPlot[Evaluate[Eqt],
 {\[Omega], -1000, 1500}, {\[CapitalOmega], -4000, 4000}]
4

In[23]:= Solve[Eqt, [Omega]]

During evaluation of In[23]:= Solve::ratnz: Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.

Out[23]= {{\[Omega] -> -707.107}, {\[Omega] -> 707.107}, {\[Omega] -> 
   0.833333 (\[CapitalOmega] - 
      1. Sqrt[1.5*10^6 + \[CapitalOmega]^2])}, {\[Omega] -> 
   0.833333 (\[CapitalOmega] + Sqrt[1.5*10^6 + \[CapitalOmega]^2])}}

In[24]:= Plot[
 0.8333333333333334` (\[CapitalOmega] + Sqrt[
    1.5`*^6 + \[CapitalOmega]^2]), {\[CapitalOmega], 0, 1000}]
5

Hi guys, I appreciate the feedback. I could figure it out by solving the equation…

Eqt = \[Omega]^4 - \[Omega]^3*\[CapitalOmega]*(Jp/
       Jt) - \[Omega]^2 ((k11/m) + (k22/
         Jt)) + \[Omega]*\[CapitalOmega]*((k11*Jp)/(m*Jt)) + ((k11*
         k22 - k12^2)/(m*Jt)) == 0;
Es = \[Omega] /. Solve[Eqt, \[Omega]]
Plot[Es, {\[CapitalOmega], 0, 1500}]

Thanks, again