Physics 332: Computational Physics
Westminster College
Spring 2012
Homework| Due | Reading | Problems | Posted |
| Due | Reading | Problems | Posted |
| Jan. 18 | Boas Chapter 8.5 | Jan. 18 | |
| Jan. 20 | Nakanishi Chapter 3.1 | Jan. 18 | |
| Jan. 23 | Boas Chapter 7.1, 7.3 and ideally 7.4-7.6 | Jan. 22 | |
| Jan. 25 | Nakanishi Chapter 3.2 | Boas 8.5.1, 8.5.4, 8.5.36, 8.5.38 | Jan. 22 |
| Jan. 27 | |||
| Jan. 30 | Nakanishi Chapter 3.3 | Boas 7.2.9, 7.5.2 by hand and Mathematica (at least the 1st 50 terms), 7.5.9 using Mathematica (again 50 terms). Nakanishi 3.1, 3.2, 3.3. | Jan. 27 |
| Feb. 1 | Jan 28 | ||
| Feb. 3 | Boas 8.6 and 7.11 | Jan 28 | |
| Feb. 6 | Nakanishi 3.6, 3.7, and 3.8. In problems 3.6, 3.7, and 3.8 you will explore the behavior of various complications to the SHO. In 3.6 you will need to find the transition between underdamped and overdamped numerically, be sure to explain your approach. In 3.7 you will need to construct an amplitude vs driving frequency plot. It will be inconvienent to do this by hand and also get enough data points for a good graph, so you should automate collecting the data. In 3.8 you will need to find the velocity for a variety of positions. This is most clearly expressed as a graph of one vs the other but other ways are also reasonable. Make sure that you include your qualitative argument. | Jan 28 | |
| Feb. 8 | |||
| Feb. 10 | |||
| Feb. 13 | |||
| Feb. 15 | Boas 7.12 | ||
| Feb. 17 | Boas 7.12 cont. | Project Proposal | |
| Feb. 20 | |||
| Feb. 22 | |||
| Feb. 24 | Boas 8.6.41 and 8.6.42-these should be analyzed both by numerical integration of the time series (i.e., y(t)) for 20 driving periods and using fourier series construct the oscillator response (Mathematica will remove some of the drudgery). Based on Nakanishi 3.10- construct a pendulum with q=0.5 Hz, l=9.8m, g=9.8m/s^2 driven at Omega_D=2/3 rad/s and using a time step of dt=0.04s. Drive this pendulum with each of the following amplitudes: F_D=0.1, 0.5, 0.99, and 1.2rad/s^2 for 200 oscillation periods. From the theta and omega data you collect construct the phase space for each oscillator (you will probably need a different graph for each driving amplitude). In addition to the phase space plot make a Poincare surface of section plot strobing once every driving cycle. Finally Boas 7.12.5, 7.12.6, and 7.12.12. | ||
| Mar. 2 | Fourier Transform of real data. You will analyze the icecore data taken at the Vostok Antarctic research station to look at some of the long term oscillations in the earth temperature which are believed to be due to oscillations in the earths orbit, called Milkankovitch cycles.. The temperature data is reconstructed from variations in the concentration of Deuterium in the ice ( degree of preferential freezing depends on temperature). Your task is to find the inverse FFT of the temperature data, graph |g(omega)| (or even better the powerspectrum) and identify which peak corresponds to which Milkankovitch cycle. To start, get the data and understand what it is (graphing it may help). Notice that the depth intervals are equal, but the time intervals are not, explain why this is. Unfortunately this complicates the process of taking a FFT as the data must be equally spaced in time. Sample the data before finding the inverse FFT, your sampling should be equally spaced in time. | ||
| Mar. 16 | Nakanishi 5.0 (in a 3D box with metal walls, 5 of which are at a potential of 0V and 1 is at a potential of 1V, find the potential using the relaxation method. Make your space 10x10x10 including the walls. Graph a slice near the center of the box that includes the wall at 1V.) and 5.1. | ||
| Mar. 21 | Exam | ||
| Mar. 23 | Nakanishi 5.6 and 5.8 |