Question

Problem 5 (15 points) A circular motion model of the drivenSHO. In the
middle of a lake, a long pole stands. The pole is firmly built ontothe bottom
of the lake. It is strong and stable, and sticks just above thewater. A bungee
cord is connected to the top of the pole, and the other end of thebungee cord
is attached to a jet ski. We do not consider any vertical motion ofthe jet ski.
Only the horizontal motion is considered. The relevant forcesacting on the jet
ski are
(1) the elastic force from the bungee cord, which we assume tobe

Fb = -k!r
(2) the damping force from the water, which we assume to be

Fr = -b!v
(3) and the thrust of the engine of the jet ski, which we assume tobe

Ft = F0 (ˆx cos(!t) + ˆy sin(!t)) .

(a) Write down the x component (or the y component) of theequation of
motion, and show that it has exactly the same form as that for thedriven
SHO problem.


(b) Assume that the jet ski is doing a circular motion with a phaseshift/lag (Delta)

r= D(x cos((Omega)t - (Delta)) + y sin((Omega)t - (Delta)))

(c)

In this rotational motion model, explain, in physical terms(the centripetal
force and the speed), why (delta) goes from 0 (for Omega = 0) toPi/2 (for Omega = OmegaNaught) to Pi (for Omega ->Infinity).