Charged ring with oscillating particle

[nautola]

Homework Statement

A ring of radius 6 cm that lies in the yz
plane carries positive charge of 7 μC uniformly
distributed over its length. A particle of mass
m carrying a charge of −7 μC executes small
oscillations about the center of the ring on its
axis with an angular frequency of 15 rad/s.
Find the angular frequency of oscillation of
the mass if the radius of the ring is doubled
while keeping the linear charge density on the
ring constant.

Homework Equations

F = kQq/r²

The Attempt at a Solution

I don't even know where to start with this one. To be honest, I'm not entirely sure what's actually going on. Is the particle going around the ring? Is it going right through it? I have no idea.

 

[rl.bhat]

Due to the simitry, the field at the centre of the ring is zero. Search for an expression for a field along the axis of a charged ring in the web. Since distance x is very small, neglect the higher power of x in the expression. Now F = E( - q) = ma. And since in SHM, a = -ω²x, you can compare the two angular velocities.