function [p] = forcer (t, ndfree)
%     * * * * * * * * * * * * * * * * * * * * * * * * * * * *
%     define forcing function for step by step integration
%     NOTE: this requires application dependent functions
%     * * * * * * * * * * * * * * * * * * * * * * * * * * * *
      p = zeros(ndfree) ;
      f2=3000.; f3=4000.; f4=-2000.; tone = 0.1;
%     transient test problem  bigg's p. 123, linear ramp (decreasing)
      foft = 0.0 ;
      if  t < tone 
        foft = 1.-t/tone ;
      end % if on ramp
      p(1) = 0.  ;
      p(2) = f2*foft  ;
      p(3) = f3*foft  ;
      p(4) = f4*foft  ;
      end % function forcer