MATLAB: Hello, how to solve this equation EIk^4-mv^2k^2+2mvwk+(m+M)w^2=0 numerically where w is variable,

how to solve fourth order equationb numerically

can we solve this for k numerically, sorry this is fourth order equation not two order

Thanks

Best Answer

Supply all the scalar parameters, then:

Eqn = @(w) E*I*k^2-m*v^2*k^2+2*m*v*w*k+(m+M)w^2;
w0 = 42;
[w,fval] = fsolve(Eqn, w0)

Experiment with the correct value of ‘w0’ to get the correct result.

EDIT — (Dec 10 2019 at 13:18)

The Symbolic Math Toolbox produces:

w = (k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)

or to calculate both roots:

w = [(k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)
     -(k*(- E*I*k^2*m - E*I*M*k^2 + 2*m^2*v^2 + M*m*v^2)^(1/2) - k*m*v)/(M + m)]

Related Solutions

MATLAB: Solve out a symbol

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

MATLAB: Symbol calculation and numerical values

You are doing things in the wrong order.

k,e,m,w are not unknowns. They are knowns. So why have you set them up as symbolic?

Next, subtract k from the right hand side. Don't set the two equal. This lets you plot the thing. ALWAYS PLOT EVERYTHING! Do that before you just throw it into a solver.

syms s
k=1; e=0.0006; m=2000; w=2*pi*10^6;
eqn = (w*sqrt(e*m/2)*sqrt(sqrt(1+(s/(w*e))^2)-1)) - k;
fplot(eqn,[-.1,.1])
yline(0);
grid on

I've plotted it over a fairly small domain. It does cross the line at y==0.

ssol = solve(eqn,s)
ssol =
 -(1288490188800*pi*3^(1/2)*18206206649565666255441706068998^(1/2))/27309309974347922922410255680009
  (1288490188800*pi*3^(1/2)*18206206649565666255441706068998^(1/2))/27309309974347922922410255680009
  
vpa(ssol)
ans =
 -0.0010954451150103438340309550004199
  0.0010954451150103438340309550004199

Yes, you could have set everything up as symbolic, then substitute the values of k,e,m,w in at the end.

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

So then read the help for subs.

help subs

Best Answer

Related Solutions

MATLAB: Solve out a symbol

MATLAB: Symbol calculation and numerical values

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