Let us assume a solution of equation(3.18) of the following form

                                                                                                                                    (3.19)

where s is a constant (can be a complex number) and t is time.

So that and , on substituting in equation (3.18), we get,

                       

From the condition that equation (3.19) is a solution for all values of t , above equation gives a characteristic equation (Frequency equation) as

                                                                                                                      (3.20)