practice

  1. Write something.
  2. Write something else.
  3. Graph the following Fourier series with enough detail that you can determine basic shape of each wave.
    1.  
    		y = Σ  1  sin(2n − 1)x  = sin x +  1  sin 3x +  1  sin 5x +  1  sin 7x +  1  sin 9x + ⋯
    2n − 1 3 5 7 9
    1.  
    		y = Σ  (− 1)n +1  sin nx  = sin x −  1  sin 2x +  1  sin 3x −  1  sin 4x +  1  sin 5x − ⋯
    n 2 3 4 5
    1.  
    		y = Σ  1  cos(2n − 1)x  = cos x +  1  cos 3x +  1  cos 5x +  1  cos 7x +  1  cos 9x + ⋯
    (2n − 1)2 9 25 49 81
  4. Write something completely different.

conceptual

  1. Walking involves the coordinated periodic motion of various parts of your body. Identify the parts of your body that are moving …
    1. in phase with each other
    2. out of phase with each other

worksheets

  1. worksheet-superposition.pdf
    These unusually shaped wave pulses are heading towards each other in a medium whose wave speed is one grid unit per second. Draw the resulting shape of the medium one, two, three, and four seconds later.