I'm working on my final project in this independent study I'm in. I worked out this problem, but I want to verify that I'm right.
A string of length L with both endpoints fixed, such as the string of a piano, is struck at its midportion, the impact thus imparting to the string an initial velocity which is defined by:
Find the motion of the string.
I set up the following boundary value problem:
and I got the following Fourier Series Solution:
Does this look right? I would appreciate any help!!!
Are you familar with how to work with Boundary Value Problems? I would post out all the steps but it will take far to much typing. It would be better if you write your work and I tell you if I agree with it or disagree. Try reading this, see if it helps you.
I was thinking it over today, and I realized where that series came from (Because I had derived it a couple weeks back...but I was tired, and didn't catch that.)
There is one question I still have: Are you sure that your is correct? I got this for
.
When I simplify the integral, this is what I'm left with:
.
Does this seem right?