Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    The Question:

    The ends x = 0 and x = L of a stretched string are fixed. The point
    p (0 < p < L) is drawn aside a distance h and, at the instant t = 0,
    the string is released from rest. Thus
    y(x, 0) = hx/p , 0<=x<p,
    =h(L−x)/(L−p) , p< x<=L
    and dy/dt(x, 0) = 0. Use separation of variables and Fourier series to find
    y(x, t).

    My Attempt
    y(x,t)=F(x)G(t)
    so c^2F''(x)/F(x)=G''(t)/G(t)=-w^2

    F''=(-w^2/c^2)F, and G''=-w^2G

    y(0,t)=y(L,t)=0 for all t>0


    I think I need to find y(x,0) as a fourier sine series, but when I tried to find an for it I got (2h/Lp)[(n(p-L)sin(np)-cos(Ln)+cos(np))/n^2] + (h/(L-p))[(npsin(np)+cos(np)-1)/n^2] which seems wrong



    I have no idea how to answer this question, can anyone outline the method I should use?

    thanks xxx
    • Thread Starter
    Offline

    0
    ReputationRep:
    anyone?
    Offline

    17
    ReputationRep:
    You need to find the fourier series over the region [0, L]. See equation 36 at http://mathworld.wolfram.com/WaveEqu...mensional.html
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 8, 2010
Poll
Do I go to The Streets tomorrow night?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.