Solution of this non-linear eqution

w= 0: 0.01: 20;

d=100

g=10

w^2=g*k*tanh(k*d)

find the values of 'k'.

Answer 1

[Dimitris Kalogiros]

Hi A. Hossain

Try this:

clear; clc;

syms w d k

d=100
g=10

for w=0:0.1:20
    fprintf('-----  w = %f -----\n', w);
    eq=w.^2==g*k*tanh(k*d) 
    vpasolve(eq)
    fprintf('\n\n');
end

Of Course, it does not provide an analytical solution, but a numerical one.