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Although two dimensional N-body simulations of disk galaxies have been done for over thirty years, we feel that the interactions between various free parameters deserve further study. As a preliminary step in validating a computer code with collisionless particles representing star clusters, colliding particles representing giant molecular clouds, and a gravitating hydrodynamic component representing the intercloud medium, we study the effects of the number of particles (10k-400k), the softening of the gravitational potential (.25-1.0 cell widths), and the grid size ($64^{2}$ and $128^{2}$) on the changes of Toomre's Q and the bar-mode (m=2) instability for the collisionless N-body component. We use a Cartesian grid with a time-centered leap frog integration scheme and a fast Fourier transform potential calculator. We find that the growth of Q and the bar mode depend sensitively on both N and the softening factor. We also find that as N increases, the amount of softening required to maintain cool systems decreases. Judicious selection of parameters can minimize growth rates of various instabilities, thereby increasing relaxation times.
