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(402)

The homogeneous algebraic system (402) accepts nontrivial solutions only if its determinant has value zero, i.e.,

$|\begin{array}{cc}-\mathrm{sin}\gamma l+\mathrm{sinh}\gamma l& -\mathrm{cos}\gamma l+\mathrm{cosh}\gamma l\\ -\mathrm{cos}\gamma l+\mathrm{cosh}\gamma l& \mathrm{sin}\gamma l+\mathrm{sinh}\gamma l\end{array}|=0$ (403)

(403)

Expansion and simplification of Eq. (403) yields

$\mathrm{cos}\gamma l\mathrm{cosh}\gamma l-1=0$ (404)

(404)

Introduce the notation

$z=\gamma l$ (405)

(405)

Substitution of Eq. (405) into Eq. ...

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