For the system described in Exercise 1, find a linear point transformation to variables in...

For the system described in Exercise 1, find a linear point transformation to variables in which the Hamilton–Jacobi equation is separable. By use of the action-angle variables, find the eigenfrequencies of the system.

Exercise 1

Two particles move in one dimension at the junction of three springs, as shown in the figure. The springs all have unstretched lengths equal to a, and the force constants and masses are shown.

Find the eigenfrequencies and normal modes of the system.