- #1
Dixanadu
- 254
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Homework Statement
Hi everyone! first post here :)
Basically, the question is as follows:
Consider a hydrogen fluoride molecule (atomic mass of H is 1g/mole and of F is 19 g/mole).
1. Write the energy of the system in terms of the displacements of both atoms.
There are other questions but if i can get this one I think the others will be fine.
Homework Equations
This is a coupled oscillator problem, so we're gona model it as two masses with a spring in between, that has a stiffness k. the equations are:
Total energy E = 1/2 kx2
General solution to the coupled oscillator differential equation: x = A cos(ωt) (we don't have to worry about phase shift)
Restoring force F by Hooke's law = -kx
The Attempt at a Solution
What I'm having trouble with is 2 things:
1st of all - my professor has written in his reference notes that the total energy E of another similar problem is 1/2 kx2. Shouldn't it be 1/2 kA2; the sum of 1/2 mv2 and 1/2 kx2?
secondly - I am a bit confused as to how I'm meant to work with the displacements - since each atom displaces in the opposite direction (I don't think there is any normal mode other than this one) how do i construct the problem? Anyway, here's what I got for a solution but I have no way of telling if its right since its an assessed assignment:
If we consider the displacement of the hydrogen atom as xH and that of the fluoride atom as xF then:
E = 1/2 kx2 = 1/2 k(xH-xF)2
So...here's the confusion now...the signs of the displacements xH and xF...what are they? @_@ and is the equation I am using even the right one?
Thanks a lot guys!