Solve Trancedental equation with two dependent variables

I'm trying to solve this Transcedental Equation,

2(1-cosh(s1*l)*cos(s2*l))+(sinh(s1*l)*sin(s2*l).*(s1/s2-s2/s1))=0 where,

s1= √(P/2EI+√((P/2EI)^2+(ρAω^2)/EI)) ,

s2= -√(P/2EI-√((P/2EI)^2+(ρAω^2)/EI))

I'm interested to find the values of ω which satisfies the above Transcedental eqaution.

Answer 1

[Roger Stafford]

Use 'fzero'. It is helpful to first make a plot of the left side of your equation as a function of omega to get an initial omega approximation for use in 'fzero' at zero-crossing point(s).