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bunkergirl198
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Differential Equation Help -- Vibrating String
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.
Gravity = -mg
Friction force on an object moving with velocity v = -[tex]\beta[/tex]v.
Well. That's the hard part :)
utt + [tex]\frac{mg+Bv+T}{\rho(x)}[/tex] uxx=f(x,t)
Initial conditons
u(x,0)=f(x)
ut(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 :)
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 :)
utt + [tex]\frac{mg+Bv+T}{\rho(x)}[/tex] uxx=f(x,t)
Initial conditons
u(x,0)=f(x)
ut(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 :)