Problems to solve:
1. Find the time dependence of the coordinates of a particle with energy E = 0 moving in a
parabola in a eld U(r) = -a/r, where a > 0 is constant.
2. Determine the e ective cross-section for scattering of particles from a perfectly rigid sphere
of radius a (the interaction is such that the potential U is in nite for r < a and null for r > a).
3. Determine the e ective cross-section for a particle to “fall” to the centre of a eld U(r) = -a/
r^2.
4. Determine the e ective cross-section for small-angle scattering in a eld U(r) = a/r^n (n >
0).
5. Two equal masses move without friction on a plate. They are connected by two springs of
equal constants. Find (a) the equations of motion, (b) the normal frequencies and (c) the
amplitude ratios of the normal vibrations and the general solution.
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6. Two mass points (equal mass m) lie on a frictionless horizontal plane and are xed to each
other and to two xed points A and B by means of springs (spring tension T, length l). Establish
the equation of motion. Find the normal vibrations and frequencies and describe the motions.