Exercise 2 A body of mass m is forced to slide without friction on an Archimedean spiral, described by r 0 in polar coordinates (see figure 2), and is subject to an elastic force F = -kr toward the centre. Figure 2: Plot of the Archimedean spiral r = ab, where 0 is allowed to be negative, and a is a real number with appropriate units. 1. How many Lagrangian coordinates are necessary to describe this system? 2. Write the Lagrangian of the system. 3. Write the equations of motion.

Exercise 2 A body of mass m is forced to slide without friction on an Archimedean spiral, described by r 0 in polar coordinates (see figure 2), and is subject to an elastic force F = -kr toward the centre. Figure 2: Plot of the Archimedean spiral r = ab, where 0 is allowed to be negative, and a is a real number with appropriate units. 1. How many Lagrangian coordinates are necessary to describe this system? 2. Write the Lagrangian of the system. 3. Write the equations of motion.