Astronomy derivation, leading to question about oscillations

[acdurbin953]

Homework Statement

The sun experiences a vertical gravitation acceleration of g=-4πGρz, where ρ is the density of the disk of our Galaxy.
a) Assuming that d²z/dt²=-kz, express k in terms of ρ and G.
b) Find the general expression for z and w=dz/dt as a function of time.
c) If the total mass density is 0.15 M_solar pc^-3, what is the oscillation period?

Homework Equations

Simple harmonic motion equations
Method of solving 2nd order diff eqns

The Attempt at a Solution

Okay, so I'm fairly lost with this problem. My initial reaction was to solve d²z/dt²=-kz, so I moved over -kz term, set it all equal to zero and got z=c₁e^√(k)t+c₂e^-√(k)t.

This doesn't at all seem right to me.
#1 I have no idea how to get k in terms of ρ and z.
#2 Wishful thinking has me hoping that my solution should resemble some type of simple harmonic motion equation, which my eqn does not look like.

Not sure how to progress with this. Any hints?

 

[BvU]

solve d2z/dt2=-kz, so I moved over -kz term, set it all equal to zero and got z=c₁e^√(k)t+c₂e^-√(k)t.

That's strange: this z doesn't satisfy the differential equation ! Try it !