Transform PDE Problem Solutions with Fourier Transforms | Get Help Now

[mike1111]

Homework Statement

Use Fourier transforms to get solution in terms of f(t) adn g(t)

Homework Equations

d⁴u + K²*d²u =0
dx⁴ (space) dt²

u(0,t)=f(t)
u'(0,t)=g(t)
u''(L,t)=0
u'''(L,t)=0

The Attempt at a Solution

I been working no it for hours the best I got is
k⁴U +K* (d²U/dt²) =0
I'm not sure where to go since i don't hve initial conditions

Really need someone to show me how to do the question or a similar one

 

[HallsofIvy]

Homework Statement

Use Fourier transforms to get solution in terms of f(t) adn g(t)

Homework Equations

d⁴u + K²*d²u =0
dx⁴ (space) dt²

u(x,0)=f(t)
u'(x,0)=g(t)
u''(L,t)=0
u'''(L,t)=0

The Attempt at a Solution

I been working no it for hours the best I got is
k⁴U +K* (d²U/dt²) =0
I'm not sure where to go since i don't hve initial conditions

Yes, you do have initial conditions! They are u(x,0)= f(t) and u'(x,0)= g(t). (I assume the ' denotes differentiation with respect to t.)

Really need someone to show me how to do the question or a similar one

 

[mike1111]

my fault, there aren't meant to be initial ocnidtion, just fixed the question