The motion of a linear oscillator may be represented by means of a graph in which x is shown as abscissa and dx/dt as ordinate. the history of the oscillator is then a curve. (a) show that for an undamped oscillator this curve is an ellipse. (b) show (at least qualitatively) that if a damping term is intro- duced one gets a curve spiraling into the origin.

Imagine that you have two balloons (or, better yet, actually inflate two balloons, if possible). create static electricity around one of the balloons by rubbing it against your hair or your sweater and then bring that balloon close to the other balloon, which has not been charged. try this with at least one other object—and for variety in the discussion, avoid using an object already described by your classmates. then, for your initial post to the discussion, answer the following questions: what happened with the two balloons?