Problem to solve simultaneous equations

Questions
,
1

Hi,
I have problems to solve simultaneous equations!
The NSolve command also does not lead to a solution.
Mathematica runs the whole night, but does not give any solutions.
Have anybody an idea?
Thanks for your help!

simultaneous equations.nb (2.8 KB)

2

After some simplifications by hand I get the expression below which one wants to set to 0 to solve for f.

16 Ds f^3 n p W^2 - 
 k^3 \[Pi]^2 Q Coth[(H k \[Pi])/(4 f W)] Sec[\[CurlyPhi]]

Without numeric values for the various parameters this is unlikely to have a “useful” solution.

3

Thank you for your help first.
Is there no general solution for this system of equations without using values for the parameters?
Even if I use values for the parameters and set the equation 0, the Solve command does not get the f out of the Coth.

solve equation.nb (3.42 KB)

4

I look carefully at this Plot

Plot[16*80*f^3*3.67*1*108.29^2-1^3/\[Pi]^2*210890*
  Coth[(20*1/\[Pi])/(4*f*108.29)]*Sec[0.445457],{f,-.2,.2}]

to estimate locations of solutions.

I then try

FindRoot[16*80*f^3*3.67*1*108.29^2-1^3/\[Pi]^2*210890*
  Coth[(20*1/\[Pi])/(4*f*108.29)]*Sec[0.445457]==0,{f,0.175}]

which returns

{f->0.171224}
5

Great, thanks for the quick help!!! :slight_smile: