# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Wed, Nov 23, 2016 9:10 AM (9 months ago)

### PDEs: 1D wave equation

assigned today:
• standard-PDEs: 1D wave equation:

I can derive and calculate the solution of a 1D wave equation.

1. 12.3.11 (triangle initial conditions)
2. 12.3.14 (non-zero velocity)
3. 12.3. 20 (clamped beam)

Due today:
• standard-fourier transform applications:

I can apply Fourier transform theory

1. Calculate the shape of a diffraction pattern for an interesting 2D mask.
2. An electron is in the lowest level of a SHO with a frequency of 10^15 Hz. Then the potential is shut off. Describe the particle's wave function after one nanosecond.
3. What is the maximum frequency response (and width of the resonance peak) for a damped system excited by a delta function with m=1, b=0.2, and k=10?

# in class

• quiz on the infinite square well and what happens to the wave function when the walls are removed.
• Had them write down what they remembered about a clamped string
• never say $$f=\frac{nv}{2L}$$ but lots of good images and notions about harmonics
• Had them consider the free body diagram of a small chunk of the string (we talked about what level to zoom in on)
• we decided to skip the analysis that leads to the wave equation
• talked basically for the rest of time about the separation of variables technique

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