homework13

Task01
Exercise 6.9:Perform a analysis of waves on a string in which one end is free to move while the other is held fixed.Assume an initial Gaussian wavepacekt located 40 percent from one end.

Abstract
the motion of wave can be described as

1.png

this equation can be applied for many situations,including waves on a string.To slove this problem

2.png

we assume a simple Gaussian plank of the string,that is

3.png 5.gif 4.gif

Background
Power spectrum we consider a string with certain boundary profile and record the displacement of a particular point on the string as a function of time,which is actually a Fourier transition.

Solution
we have values

and excited 45 percent from the fixed end. plot2 plot5 we can see from the plot,with only one end fixed,the signal is positive all the time, that is,there is no inversion in this situation. and when excited at ,there is a max peak at 1500Hz. plot3 plot4

comparing between the three plots,we can know that when excited at

,there is no peak at 1500HZ and the spectrum is symmetric.

Conclusion
when the wave reaches at a fixed end,there will be a inversion of amplify.So when only one end fixed,no inversion there.

Reference
Computational Physics : Second Edition Code from perfect Wuyuqiao