Re: Jumping Passengers on Rough Road part 2

It is certainly true that to do a detailed analysis of the dynamical
behavior of the bus would require considering the effects of the springs
and the shock absorbers.  I do not want to consider those details here,
however.  The essentials of the effect are that the bus should have its
engine in the front, so that the center of mass of the bus is close to the
front, and that the shock absorbers should be weak and the springs should
be strong, so that the suspension is underdamped.  Then, when the bus is
pitching up and down it rotates about the center of mass.  Thus, the back
of the bus is moving up and down through a longer distance than the front
is, because it is farther away from the center of mass.  This forces the
acceleration at the back to have a larger magnitude than the acceleration
at the front.  (Note that the sign of the acceleration is opposite, because
the front is moving down while the back is moving up, and vice versa.)

As Albert Einstein said, "We should try to make everything as simple as
possible, but no simpler!"