Don't leave the assignment until the night before. You won't be able to
do it in one evening...
Send e-mail if you get totally stuck.
- Follow examples 2.3.3 or 2.3.4; expand the potential in a Taylor series
about the equilibrium position and equate the coefficient to the
- Try writing vx=dx/dt x = d/dt(x2/2) and integrate to
get x(t) ~ tan κt where κ is some constant that you
- Should be straight forward...
- Follow example in section 3.7 or the lecture notes starting on p.85a; ignore terms that are second order in b.
- Calculate r for the nearest 6 atoms in terms of the equilibrium
separation d and the displacement (x,y,z). This question
is from the text - follow the advice in the text. Only calculate
d2V(r)/dx2 - the ones for the y
and z derivatives are the same by symmetry arguments. Check
your algebra using mathcad or whatever tools you have at your
- Very close to the example 4.6.1 which was discussed in class
- Similar to previous question once you introduce a new variable u
such that x = uv which makes z = (u^2-v^2)/2. At the
bottom of the loop, u=0. Use energy convservation to calculate
du/dt. Calculate d2z/dt2 at the
bottom of the loop and consider the z-component of the equations of
motion to get the reaction force.