More generally anything that hangs with little friction
from a pivot-point
can oscillate with simple harmonic motion if the angle
of oscillation is small enough. If we denote the moment
of inertia about the pivot point by I and distance from the
pivot point to the center of mass by r then Newton's
second law in rotational form reads:
In the small angle limit we can approximate 
which gives us
This differential equation has exactly the same form as
the general differential equation a mechanical system with a linear
restoring force for which we know the solutions to be
where the resonance frequency is
