According to Hooke’s Law, the restoring force decreases in magnitude as the spring is 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
