(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Astrophysic problem set

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