Homework 5

Homework 5#

Note

You are free to discuss these questions with your classmates and on our class slack, but you must write your own solutions, including your own source code.

All code should be uploaded to Brightspace along with any analytic derivations, notes, etc.

1. Pendulum#

In homework 3 you integrated a pendulum without using the small-angle approximation.

Now let’s take the FFT!

Your task

  • Recreate solution for the \(\theta_0 = 100^\circ\) evolution, \(\theta(t)\), by integrating the system for 1 period (you can use the expression for the finite-amplitude period or just the small-angle value, \(T = 2\pi\)).

    This will result in a series of points in the time-domain that we’ll call \(\theta_n\).

  • Compute the FFT of \(\theta(t)\),

    \[\Theta_k = \mathcal{F}(\theta_n)\]

    You can use a library (like numpy.fft.rfft) or my DFT code from class (I provided a python and C++ implementation).

  • Plot \(|\Theta_k|\) vs. \(\nu_k\), where \(\nu_k\) is the frequency—is the power where you expect it should be?

  • Repeat this for the same problem, but now integrating for 10 periods—how does the FFT change?

You are free to use my homework 3 solutions for the integration if you had difficulty with the assignment originally.

2. Git practice#

Let’s get some practice with git. Here is a git repository on github that we looked at in class.

ast390-sbu/test-repo

You should make sure that you have a github account.

Your task

  • Fork this repository: ast390-sbu/test-repo

    This will create a version of the git repo under your account.

  • Clone your fork.

  • Create a change to the repo, for example, add your name to the README.md file or add a file of your own to the repo. Whatever you wish.

  • add and commit your change and push your change back to your fork.

  • From the github page for your fork, create a pull request to the original repository.

Tip

We are essentially doing this sequence from class: https://zingale.github.io/computational_astrophysics/git/pull-requests.html

If you did it in class while following along then you are done.

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