Fourier sine series for a triangular wave on a finite string

[nazmus sakib]

Homework Statement

A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn.

Homework Equations

what should i use for U0(x) ?

The Attempt at a Solution

 

[BvU]

Hello nazmus,

ax from 0 to L/2 and x(1-x) from L/2 to L . Oops , I'm not supposed/allowed to give direct answers !

 

[LCKurtz]

Homework Statement

A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn.

Homework Equations

what should i use for U0(x) ?

First, you need to know what the "small" displacement is. Let's say you lift the center by an amount $h$, so the center of the string is at $(\frac L 2,h)$. Now just find the equation of the two straight line segments forming the triangular displacement. Also, I would ignore BvU's answer which is a) discontinuous and b) partially parabolic.

 

[BvU]

Also, I would ignore BvU's answer which is a) discontinuous and b) partially parabolic.

No, it was just a typo. I (of course) meant

ax from 0 to L/2 and a(L-x) from L/2 to L
​

And for the Fourier coefficient calculation it really doesn't matter how big a (or h) is.

All lin good spirit

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