State how many degrees of freedom the following systems have. In each case indicate appropriate generalized coordinates which can be used to describe the motion. (You cannot just say that the generalized coordinates are "r", "0" etc. You should indicate what they are using diagrams.) (a) A particle constrained to move on a plane. (b) A spring pendulum contained in the (x, y) plane, where a mass is attached to an endpoint of a spring of elastic constant k and equilibrium length 1. The other endpoint of the spring is fixed at the origin. (c) A (pointlike) satellite moving in the gravitational field of Earth.

State how many degrees of freedom the following systems have. In each case indicate appropriate generalized coordinates which can be used to describe the motion. (You cannot just say that the generalized coordinates are "r", "0" etc. You should indicate what they are using diagrams.) (a) A particle constrained to move on a plane. (b) A spring pendulum contained in the (x, y) plane, where a mass is attached to an endpoint of a spring of elastic constant k and equilibrium length 1. The other endpoint of the spring is fixed at the origin. (c) A (pointlike) satellite moving in the gravitational field of Earth.