
Natural frequency (or called Characteristic Frequency)

That is the frequency at which a system would oscillate by itself
if displaced. The natural frequency of a springmass system is f_{o}= √(k/m)/2π,
where k is the spring constant and m is the mass of the object attached to the spring.

Forced oscillation

A periodic force at a given frequency (called driving frequency f_{d})
is applied to an oscillating system of natural frequency f_{o}.
At the beginning (transient stage), there is a mixture of two kinds of oscillations,
one has the frequency f_{o} and the other has f_{d}. The former will gradually die out
because of the damping effect. Eventually (at the steady state) the system settles
down with oscillation at the frequency of the driving force (f_{d}).

At the transient stage, the object responds to two oscillations (f_{o} and f_{d}),
the superposition of them forms a BEAT.

Resonance

When the driving frequency is at the same frequency as
the natural frequency of the oscillator, the amplitude of oscillation
is at its greatest. When this happens the energy of the oscillator becomes a maximum.

Phase

When f_{d} << f_{o}, the responder is in phase with the driver.
When f_{d} = f_{o}, the responder lags the driver by 90^{0}.
When f_{d} >> f_{o}, the responder and the driver are in antiphase.
