1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    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

    [tex]
    \frac{d^2z}{dt^2} +v^2z = 0
    [/tex]
     
  4. Oct 29, 2008 #3
    Yes your correct about the original equation...also not sure why they used v for the angular velocity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Astrophysic problem set
  1. Problem Set Three (Replies: 0)

  2. Problem Set 4 (Replies: 0)

Loading...