- #1

bunkergirl198

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**Differential Equation Help -- Vibrating String**

## Homework Statement

Suppose a tightly stretched vibrating string has a variable density [tex]\rho[/tex](x). Assume that the vibration is small and is only in the vertical direction (transverse-vibration). Derive teh PDE taking into consideration the gravity and the frictional force.

## Homework Equations

Gravity = -mg

Friction force on an object moving with velocity v = -[tex]\beta[/tex]v.

## The Attempt at a Solution

Well. That's the hard part :)

u

^{tt}+ [tex]\frac{mg+Bv+T}{\rho(x)}[/tex] u

_{xx}=f(x,t)

Initial conditons

u(x,0)=f(x)

u

_{t}(x,0)=g(x)

Boundary conditions

u(0,t)=0

u(l,t)=0

I don't really think my differential equation is right, now do I know how to derive it. It was just my spin on an equation I came across a while ago (if I knew what it was I'd cite it.)

Thanks for ANY help :)