Homework Help: Very stuck on electrostatics question

State Gauss' Law

A spherical volume carries a uniform charge density [itex]\rho_0[/itex]. A particle of mass m and charge -q is placed inside the sphere at radial distance r. (This additional charge does not distort the field arising from the [itex]\rho_0[/itex] charge density.) Show that the particle oscillates harmonically and find its' oscillation frequency.

don't really know what to do here.

obviously gauss' law is [itex]\nabla \cdot \vec{E}=\frac{\rho_0}{\epsilon}[/itex]
and the lorentz force will probably come into play, [itex]F=\int_V \rho_0 \vec{E} dV[/itex] seeing as ther's no magnetic field.

but i can't put it together.

thanks guys.

 

yeah. just got it there actually. thanks though. took me flippin ages!