## Assignment #6

### Question #1

You shouldn't need a hint for this one.

### Question #2

Consider introducing a fourth generalized coordinate that represents the
position of the pulley attached to the string of length l1. Then you will
have four generalized coordinates and two equations of constraints relating
them to the lengths of the strings. The solution is a straight forward
solution of a system of equations but it gets quite involved. Just setting
up the system is good enough.
### Question #3

First work out Lagrange's equations. Solve for the equilibrium angle, theta0,
by setting d^2 theta/dt^2 = 0. Then expand theta about theta0 to first order
in some small angle. It should end up looking like a typical harmonic
oscillator problem.
### Question #4

Actually, the translation and rotation modes decouple so you won't need
to work out any determinants in this case. This wouldn't necessarily be
the case if the springs had different spring constants or if the springs
weren't equally spaced on either side of the center of mass.