Every pendulum is “born” with a natural frequency. This frequency (and period) is not affected by the amplitude of oscillation.

The natural frequency of a spring-mass system depend on the stiffness (the spring constant of the spring) and the inertia (the mass of the mass) of the system.

–

The formula for the spring-mass system can be derived in just a few lines from N2L.

–

The natural frequency of a pendulum is dependent only on its length. (The acceleration of free fall is the other factor, but we usually cannot choose the value of g.)

–

Very intricate patterns can be traced out by a “double pendulum”. See the pendulum showing off its artistic streak below.

–

The CRO (cathode ray oscilloscope) goes artistic too.