An initial conditions problem is addressed by first transforming it into a boundary value one. An appropriate functional and an extremizing sequence are proposed. The methodology has been previously named WEM (Whole Element Method) by the authors. In the present paper, this name is justified since division of the time domain is avoided even when loads with finite number of impulses of arbitrary duration are involved. The method is theoretically founded by theorems and corolaries. Their statements are included in the work. A numerical example of an undamped single degree of freedom (SDOF) system subjected to a rectangular impulse load is carried out. Comparison is made with the well-known classical solution.