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Homework Help: Astrophysic problem set

  1. Oct 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Vertical equation for motion:

    [tex]\frac{d^2z}{dt^2} +v^2 = 0[/tex]

    which corresponds to a simple harmonic oscillator, with an angular frequency [tex]v = \sqrt{4 \pi G \rho}[/tex]. The solution of the diff eq can be written as [tex]z(t) = Asin(vt+\phi_0)[/tex]

    where z(t) is the vertical position of a test particle, A is the amplitude of its motion, and [tex]\phi_0[/tex] is its initial phase.

    Given z(t), write out the expression for the vertical velocity.

    2. Relevant equations

    3. The attempt at a solution

    Since z(t) is the vertical position, the derivative of z(t) with respect to t would be the velocity? Correct?

    And the vertical velocity expression would be [tex]\frac{dz}{dt} = Acos(vt+\phi_0) * v[/tex]? Is this correct?
  2. jcsd
  3. Oct 29, 2008 #2


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    Staff Emeritus
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    Homework Helper

    Yes, that's correct.

    Just as an aside, most people and most textbooks use ω for angular velocity, so instead of "vt" those terms would be ωt.

    Also, I think the original equation is

    \frac{d^2z}{dt^2} +v^2z = 0
  4. Oct 29, 2008 #3
    Yes your correct about the original equation...also not sure why they used v for the angular velocity.
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