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Astronomy derivation, leading to question about oscillations

  1. Apr 8, 2015 #1
    1. The problem statement, all variables and given/known data
    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 Msolar pc-3, what is the oscillation period?

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

    3. 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?
     
  2. jcsd
  3. Apr 8, 2015 #2

    BvU

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