Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    9
    ReputationRep:
    Would appreciate some help with the above question.

    For part a, i believe i correctly determined the separable solutions to be

    X=cos(αx) or sin(αx)
    T=cos(αct) or sin(αct)
    Where alpha is just a constant

    So a linear combination of these would be

    y(x,t)=(Acos(αx) + Bsin(αx))(Ccos(αct) + Dsin(αct))

    However when I apply the conditions given I can't seem to get any of the constants out, Im not sure if the solution I've found is wrong or if im not applying the conditons correctly, I would appreciate any help.

    Thanks.
    Offline

    11
    ReputationRep:
    (Original post by Eremor)
    Would appreciate some help with the above question.

    For part a, i believe i correctly determined the separable solutions to be

    X=cos(αx) or sin(αx)
    Doesn't the second boundary condition restrict this to X=\sin x, so that you have:

    So a linear combination of these would be

    y(x,t)=(Acos(αx) + Bsin(αx))(Ccos(αct) + Dsin(αct))
    y(x,t)=\sin x(A \cos \alpha ct + B \sin \alpha ct) ?
 
 
 
Poll
Who is your favourite TV detective?

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.