Frequency is given in units of cycles per second, or hertz (Hz).
Potential Energy
The potential energy of a spring ( ) is sometimes called elastic energy, because it results from
the spring being stretched or compressed. Mathematically, is defined by:
The potential energy of a spring is greatest when the coil is maximally compressed or stretched,
and is zero at the equilibrium position.
Kinetic Energy
SAT II Physics will not test you on the motion of springs involving friction, so for the purposes of
the test, the mechanical energy of a spring is a conserved quantity. As we recall, mechanical
energy is the sum of the kinetic energy and potential energy.
At the points of maximum compression and extension, the velocity, and hence the kinetic energy,
is zero and the mechanical energy is equal to the potential energy, Us=^1 / 2.
At the equilibrium position, the potential energy is zero, and the velocity and kinetic energy are
maximized. The kinetic energy at the equilibrium position is equal to the mechanical energy:
From this equation, we can derive the maximum velocity:
You won’t need to know this equation, but it might be valuable to note that the velocity increases
with a large displacement, a resistant spring, and a small mass.
Summary
It is highly unlikely that the formulas discussed above will appear on SAT II Physics. More likely,
you will be asked conceptual questions such as: at what point in a spring’s oscillation is the kinetic
or potential energy maximized or minimized, for instance. The figure below summarizes and
clarifies some qualitative aspects of simple harmonic oscillation. Your qualitative understanding of
the relationship between force, velocity, and kinetic and potential energy in a spring system is far
more likely to be tested than your knowledge of the formulas discussed above.