Summary: HOME-MADE HOMEWORK FOR WEEK 6
MATH2574H, SPRING 2012, UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
Kitty on a bungee
The cat who was such a good sport the last time around is now resting peacefully
and motionlessly in a comfortable basket suspended at the end of a very long bungee
cord. The cord is extended 8 feet beyond its natural length. The terminal velocity
for kitty-and-basket is 40 ft/sec. Suppose now that the basket is raised up 4 feet
and then released with zero initial velocity.
(i) Find kitty's position y(t) at time t after release, letting y = 0 correspond to
the neutral position at which the basket hangs motionless. Start by setting up an
appropriate initial value problem.
(ii) What is the interval of time between returns to the neutral position?
(iii) Roughly how long does it take until the range of motion of the basket settles
down to less than one foot up or down from the neutral position?
Date: February 20, 2011.