PHYS 35100 - FALL 2024

Homework Set 5

Due Dec 11th via Blackboard submission, before 12:00 pm.

[PDF version of this is here: HW-5.pdf]

Instructions: Prepare responses to the following questions. Each one is worth the same amount. [A] means that a problem is meant to be done analytically, i.e. with paper and a pencil. [C] means that the problem is meant to be done with computationally, i.e. with software* Homework sets will be submitted electronically. Please submit one pdf document that contains all the work you want me to see. For the [A] ones, please scan your original, handwritten work and include in the pdf. For [C] problems, save your code/notebook as a pdf (not a screenshot) and include that pdf in the submission. Also link to the Colab notebook online and make sure it is viewable/commentable by me (jhedberg@ccny.cuny.edu). Please title your submission PHYS35100-HW5-LASTNAME-FIRSTNAME.pdf.

1. Foucault Pendulum

   Make sure you understand all the parts of the equation on this slide: Foucault Pendulum Equation of Motion, and make sure you understand the steps that got us to the final equation (with approximations): \begin{eqnarray} \eta(t) & = & x(t) + iy(t) \\ & = & A e^{-i \Omega_z t} \cos (\omega_0 t) \end{eqnarray}

   1. Make a plot that tries to replicate the demo pendulum set up we watched in class. Make some reasonable estimates for things, and create a parametric plot showing the motion of the pendulum as one would see looking down in the rotating frame. (Here's the video I took: Demo Pendulum )
   2. Now, make a real foucault pendulum. If the pendulum was located in NYC, and had a length of 8 meters, how many oscillations (i.e. and back and forths) of the pendulum would occur during one complete rotation of the Foucault Pendulum? (You can try and plot this too, but you'll quickly see that it's not very useful since there are a lot of oscillations)

* This means that I'd like you to extend the techniques we use, and not use other software, libraries, etc. That means for plotting, use matplotlib, not plotly for example.