A test question on yesterday's exam involved periodic motion. I offered the
example of an object bobbing up and down on a spring suspended from above as
an example of periodic motion. Several questions were asked about
velocities, accelerations, and forces when the object was in various
positions. One question asked what the acceleration of the object was when
it had returned to the equilibrium position on the way up. I was looking to
hear answers and reasoning such as -- At this point the forces are balanced,
there is no net force, therefore no acceleration. A particularly bright
student responded as follows.
"This is a tough one. Because the forces are balanced, there should be
constant velocity (no acceleration). However velocity is never constant in
this situation, so the best way to describe acceleration is that it is
transferring from positive acceleration to negative acceleration."
I had not thought about the problem as thoroughly as he did. I like it when
my students stretch my thinking! I know we have had discussion of
situations similar to this over the past few days but I was wondering what
others thought the best answer to this question would be. Is acceleration
simply undefined at this point?