Due: 18 November 2016
36. page 385, 7.12.18
37. page 385, 7.12.22
38. page 632, 13.3.3
39. page 662, 13.9.4
40. A stretched string extends from x = -∞ to +∞. Between
x = 1 and 2, it is displaced forming a waveform with shape -sin(πx).
The string is then
released from rest. Find the subsequent motion
using d'Alembert's solution for the wave equation.
Sketch the motion at several subsequent times. Suppose that the
string is not displaced initially but is instead struck with a mallet,
giving it an initial velocity impulse of cos(πx) between x = 1 and 2. Find
the motion of the string and sketch it at several subsequent times.
41. Verify properties 1 through 7 of Fourier transforms given in class.