IV. The program

        IV.1 Listing of the program

        Two case can be treated by the program: the free oscillations mode and the forced oscillations mode. In the case of the forced oscillations mode, the exciting force is a sinusoidal force. If the operator chose this case, he has to give the value of the exciting force's frequency. In every case, he has to enter the time step and the final time of the simulation. The other parameter are fixed, but the user can open the program to modify some values.

        IV.2 The initial conditions

        As one has previously seen, one has for the free oscillations two self modes:
- for the first mode,  = 0  so one has U(0)= 0 . Moreover, the system is not impulsed, so . If one considers that the value of the derived function at t= 0 is defined by ,  one has U(1) = U(0) = 0.
- for the second mode,  = cte  so one has U(0)= cte and  so = 0, which means
U(1) = U(0) = cte.

        For the forced oscillations mode, one has in every case  = 0 so U(0)= 0. But for the value of the derived function at t = 0, several cases are possible. The value of U(1) defines the type of the solution: real, imaginary or imaginary pure. In the upper listing, the value of U(1) has been choiced to give real solution.