  We analyse a supersymmetric mechanical model derived from (1+1)-dimensional
field theory with Yukawa interaction, assuming that all physical variables take
their values in a Grassmann algebra B. Utilizing the symmetries of the model we
demonstrate how for a certain class of potentials the equations of motion can
be solved completely for any B. In a second approach we suppose that the
Grassmann algebra is finitely generated, decompose the dynamical variables into
real components and devise a layer-by-layer strategy to solve the equations of
motion for arbitrary potential. We examine the possible types of motion for
both bosonic and fermionic quantities and show how symmetries relate the former
to the latter in a geometrical way. In particular, we investigate oscillatory
motion, applying results of Floquet theory, in order to elucidate the role that
energy variations of the lower order quantities play in determining the
quantities of higher order in B.
