# Fourier Series and Wave

1. Nov 17, 2004

### daydreaming1989

Can someone give me some hints on this problem please?

A string (length L) clamped at both ends and initially at rest, the boundary conditions for the wave function y(x,t) are:

y(x,0)=y(0,t)=y(L,t)=dy/dt(x,0)=0

A note is obtained by striking the string with a hammer at some point a, with 0,a,L. In this case dy(x,0)/dy=0 for all of the string except for the interval (a-e)<x<(a+e), where a momentum p is given to the string by the hammer. Write the Fourier representation for y(x,t) and solve for the foefficients in terms of p, L, a, d(linear density) and c=sqrt(T/d) using the limit e->0.

And the general form of motion is given by,

y(x,t)= summation (n=1-> infinity) {sin(3.14nx/L)[Acos(3.14nct/L)+Bsin((3.14nct/L)]}
where c is the veolcity of the wave shape.

Thank you very much~

Last edited: Nov 17, 2004