Introduction to SAT II Physics - FreeExamPapers

You’ll notice that the restoring force for the pendulum, mg sin , is not directly proportional to the
displacement of the pendulum bob, , which makes calculating the various properties of the
pendulum very difficult. Fortunately, pendulums usually only oscillate at small angles, where sin
. In such cases, we can derive more straightforward formulas, which are admittedly only
approximations. However, they’re good enough for the purposes of SAT II Physics.
Period
The period of oscillation of the pendulum, T, is defined in terms of the acceleration due to gravity,
g, and the length of the pendulum, L:
This is a pretty scary-looking equation, but there’s really only one thing you need to gather from
it: the longer the pendulum rope, the longer it will take for the pendulum to oscillate back and
forth. You should also note that the mass of the pendulum bob and the angle of displacement play
no role in determining the period of oscillation.
Energy
The mechanical energy of the pendulum is a conserved quantity. The potential energy of the
pendulum, mgh, increases with the height of the bob; therefore the potential energy is minimized
at the equilibrium point and is maximized at
. Conversely, the kinetic energy and
velocity of the pendulum are maximized at the equilibrium point and minimized when
.
The figure below summarizes this information in a qualitative manner, which is the manner in
which you are most likely to find it on SAT II Physics. In this figure, v signifies velocity,
signifies the restoring force,
signifies the tension in the pendulum string, U signifies potential
energy, and KE signifies kinetic energy.
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