How can i solve this equation ?

Hi

How ca i solve the attached equation to find lamda ?

When all the other terms are known.

Answer 1

[Jorge Mario Guerra González]

If you want to get multiple answers use vpasolve function. Set the number of answers you want yo get and the code will pick some then in a random way.

 syms lambda
Mt=1;    % The value of your variables
m=1;
L=1;
lt=1;
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
for n = 1:50 
  vpasolve(eqn,lambda,'random',true) 
end

this example gives you 50 answers. The answer before gives the first it finds.

[Mallouli Marwa]

 I obtain this error :

Undefined function 'vpasolve' for input arguments of type 'sym'.

[Mallouli Marwa]

How can i display this result in a vector

for n = 1:50 vpasolve (eqn,lambda,'random',true) end

[Jorge Mario Guerra González]

 syms lambda
Mt=1;    % The value of your variables
m=1;
L=1;
lt=1;
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
k=zeros(1,50);
for n = 1:50 
  k(i)=vpasolve(eqn,lambda,'random',true) 
end

that should create the vector

Answer 2

[Jorge Mario Guerra González]

Just use the function solve, which uses numerical techniques to find variables.

try this.

syms lambda
Mt=1;    % The value of your variables
m=1;
L=1;
lt=1;
%check if I wrote this correctly
eqn= 1+(cos(lambda)*cosh(lambda))+((lambda*Mt/(m*L))*(cos(lambda)*sinh(lambda)-sin(lambda)*cosh(lambda)))-((lt*lambda^3)/m*L^3)*(cosh(lambda)*sin(lambda)+sinh(lambda)*cos(lambda))+ ((Mt*lt*lambda^4)/m^2*L^4)*(1-cosh(lambda)*cos(lambda)) ==0;
value=solve(eqn,lambda) %solution for lamda

[Mallouli Marwa]

This equation must have an infinite solutions but this method show only one solution.

[John D'Errico]

You cannot find an infinite number of solutions. If you tried to write them all down, it would take infinitely long.