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NeedPhysHelp8
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Homework Statement
An atom of mass m is bonded to surface immobile body by electromagnetic forces. The force binding the atom to the surface has the expression:
F= exp\ (a\cos z + b\sin z) + d\tan(z)
where a,b, and d are constants and z is upwards. The equilibrium point is defined to be z=0. The system is subject to Earth's gravity
For small oscillations, give an approximate expression for the binding force on the atom.
The attempt at a solution
Ok so in class we were taught to do the Taylor Series expansion on F(x) and keep the linear term so you can get something that looks like F=-kx . So I got this after doing Taylor Series expansion:
where F' = (-a\sin z + b\cos z) exp\ (a\cos z + b\sin z) + d\sec^2 (z) then evaluate at z=0 then final result is :
F(z)= (b exp(a) + d )z
Since F(0) is always 0 at the equilibrium I took that out of Taylor series and ignored higher order terms.
Now I'm not sure if I'm going about this the right way? Can someone please tell me if I did this right or not? Much appreciated I love this forum!
An atom of mass m is bonded to surface immobile body by electromagnetic forces. The force binding the atom to the surface has the expression:
F= exp\ (a\cos z + b\sin z) + d\tan(z)
where a,b, and d are constants and z is upwards. The equilibrium point is defined to be z=0. The system is subject to Earth's gravity
For small oscillations, give an approximate expression for the binding force on the atom.
The attempt at a solution
Ok so in class we were taught to do the Taylor Series expansion on F(x) and keep the linear term so you can get something that looks like F=-kx . So I got this after doing Taylor Series expansion:
where F' = (-a\sin z + b\cos z) exp\ (a\cos z + b\sin z) + d\sec^2 (z) then evaluate at z=0 then final result is :
F(z)= (b exp(a) + d )z
Since F(0) is always 0 at the equilibrium I took that out of Taylor series and ignored higher order terms.
Now I'm not sure if I'm going about this the right way? Can someone please tell me if I did this right or not? Much appreciated I love this forum!
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