# Astrophysic problem set

1. Oct 29, 2008

### nissanztt90

1. The problem statement, all variables and given/known data

Vertical equation for motion:

$$\frac{d^2z}{dt^2} +v^2 = 0$$

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

where z(t) is the vertical position of a test particle, A is the amplitude of its motion, and $$\phi_0$$ 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 $$\frac{dz}{dt} = Acos(vt+\phi_0) * v$$? Is this correct?

2. Oct 29, 2008

### Redbelly98

Staff Emeritus
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

$$\frac{d^2z}{dt^2} +v^2z = 0$$

3. Oct 29, 2008

### nissanztt90

Yes your correct about the original equation...also not sure why they used v for the angular velocity.