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# Differential Equations - waves watch

1. A string is stretched to a tension T and its ends x = 0 and x = L are
attached to rings of mass M which are free to slide on parallel smooth
wires which are perpendicular to the string. Show that the transverse
displacement must satisfy the conditions:

at x=0 and at x=L

and that the normal frequencies are the numbers

where

Now I think I can show the first bits but it is getting the normal frequencys bit which I am strugglind with. The example in the notes which is almost similar is that of a weighted string and in this they split it the problem into two halves - the left and right of the mass. I don't know how to split this one up though.

Thanks in advance for any help.
2. Wnat is c here? Does your string have mass?
3. (Original post by DFranklin)
Wnat is c here? Does your string have mass?
The string doesn't have a mass and I think c is from the equation

4. (Original post by The Muon)
The string doesn't have a mass and I think c is from the equation

But the derivation of that equation usually involves the mass of the string - specifically, , where T is the tension and \rho the mass per unit length.
5. (Original post by DFranklin)
But the derivation of that equation usually involves the mass of the string - specifically, , where T is the tension and \rho the mass per unit length.
Just gone through my notes and looking at the earlier stuff I have

Flexible string
Stretched to tension T
mass density \rho
small vibrations
Gravity and air resistance ignored.
6. Not sure, but I would guess a solution of form y = sin(Ax+B) cos Ct and solve for A, B and C.

You can relate A and C immediately by the standard wave equation (which applies when you're not at the end points). And then the end point conditions give you conditions on A and B, from which you should be able to get the equation they give. I hope.

(Of course, the guess about the forum of solution might be wrong as well).

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