compressed. Consequently, the net force downward is greatest at and the net force
upward is greatest at.
Energy
The mechanical energy of the vertically oscillating spring is:
where is gravitational potential energy and is the spring’s (elastic) potential energy.
Note that the velocity of the block is zero at and , and maximized at the
equilibrium position, x = –h. Consequently, the kinetic energy of the spring is zero for
and and is greatest at x = –h. The gravitational potential energy of the system increases
with the height of the mass. The elastic potential energy of the spring is greatest when the spring is
maximally extended at and decreases with the extension of the spring.
How This Knowledge Will Be Tested
Most of the questions on SAT II Physics that deal with spring motion will ask qualitatively about
the energy or velocity of a vertically oscillating spring. For instance, you may be shown a diagram
capturing one moment in a spring’s trajectory and asked about the relative magnitudes of the
gravitational and elastic potential energies and kinetic energy. Or you may be asked at what point
in a spring’s trajectory the velocity is maximized. The answer, of course, is that it is maximized at
the equilibrium position. It is far less likely that you will be asked a question that involves any sort
of calculation.
Pendulums
A pendulum is defined as a mass, or bob, connected to a rod or rope, that experiences simple
harmonic motion as it swings back and forth without friction. The equilibrium position of the
pendulum is the position when the mass is hanging directly downward.
Consider a pendulum bob connected to a massless rope or rod that is held at an angle from
the horizontal. If you release the mass, then the system will swing to position and back
again.