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Plot a quartic expression with two variables?

Joao Pedro Duveen

Posted 7 years ago

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 m = 10; Jp = 2; Jt = 1.2; l = 0.2; k12 = 0; ka = 2.5(10^6); k11 = 2ka; k22 = (0.5^2 + 0.5^2)ka; Eqt = \[Omega]^4 - \[Omega]^3\[CapitalOmega](Jp/ Jt) - \[Omega]^2 ((k11/m) + (k22/ Jt)) + \[Omega]\[CapitalOmega]((k11Jp)/(mJt)) + ((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,

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

The idea is to get a graph similar to this one:

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,

POSTED BY: Joao Pedro Duveen

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Joao Pedro Duveen

Posted 7 years ago

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]((k11Jp)/(mJt)) + ((k11* k22 - k12^2)/(m*Jt)) == 0; Es = \[Omega] /. Solve[Eqt, \[Omega]] Plot[Es, {\[CapitalOmega], 0, 1500}] Thanks, again

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

POSTED BY: Joao Pedro Duveen

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 7 years ago

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[1.510^6 + \[CapitalOmega]^2])}, {\[Omega] -> 0.833333 (\[CapitalOmega] + Sqrt[1.510^6 + \[CapitalOmega]^2])}} In[24]:= Plot[ 0.8333333333333334` (\[CapitalOmega] + Sqrt[ 1.5`*^6 + \[CapitalOmega]^2]), {\[CapitalOmega], 0, 1000}]

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}]

POSTED BY: Frank Kampas