Solve out a symbol

Hi I have the formula :

k=w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1)

And I will solve out s:

clc
clear all

syms k w m e s

k=w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1)
solve(k,s)

But the problem is this :

Warning: The solutions are valid under the following conditions: e ~= 0 & w ~= 0. To include parameters and

conditions in the solution, specify the 'ReturnConditions' option.

> In solve>warnIfParams (line 517)

In solve (line 360)

ans=0

Can I get s by using Matlab?

Answer 1

[infinity]

Hello,

If you write

solve(k,s)

the solve function will solve another equation k == 0, i.e,

w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1) == 0

which is not what you want to solve. Also, obviously, s = 0 is the solution of this equation.

So, you may change your code litle bit as follows

clc
clear
syms k w m e s

f=w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1)

[sol,~,conditions] = solve(f==k,s,'ReturnConditions', true)

It will give the results

sol =
 
 -(2*k*(k^2 + e*m*w^2)^(1/2))/(m*w)
  (2*k*(k^2 + e*m*w^2)^(1/2))/(m*w)
 
 
conditions =
 
 signIm((k*1i)/(w*((e*m)/2)^(1/2))) == 1 & signIm((k^2*2i)/(e*m*w^2) + 1i) == 1
 signIm((k*1i)/(w*((e*m)/2)^(1/2))) == 1 & signIm((k^2*2i)/(e*m*w^2) + 1i) == 1

[Pouyan Msgn]

Thank you! I could also solve it by this way:

clc
clear all

syms k w m e s

eqn=k==[w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1)]
%k=1; e=0.0006; m=2000; w=2*pi*10^6;
sol=solve(eqn,s)

which gave me the same answer