Very stuck on electrostatics question

[latentcorpse]

State Gauss' Law

A spherical volume carries a uniform charge density \rho_0. 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 \rho_0 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 \nabla \cdot \vec{E}=\frac{\rho_0}{\epsilon}
and the lorentz force will probably come into play, F=\int_V \rho_0 \vec{E} dV seeing as ther's no magnetic field.

but i can't put it together.

thanks guys.

 

[Cyosis]

What is the equation of motion for a harmonic oscillator? Compare the equation of motion of a harmonic oscillator to the equation of motion you have for this given problem. It should strike you as very similar.

 

[latentcorpse]

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