  Forced oscillation of a system composed of two pendulums coupled by a spring
in the presence of damping is investigated. In the steady state and within the
small angle approximation we solve the system equations of motion and obtain
the amplitudes and phases of in terms of the frequency of the sinusoidal
driving force. The resonance frequencies are obtained and the amplitude ratio
is discussed in details. Contrary to a single oscillator, in this two-degree of
freedom system four resonant frequencies, which are close to mode frequencies,
appear. Within the pass-band interval the system is shown to exhibit a rich and
complicated behaviour. It is shown that damping crucially affects the system
properties. Under certain circumstances, the amplitude of the oscillator which
is directly connected to the driving force becomes smaller than the one far
from it. Particularly we show the existence of a driving frequency at which the
connected oscillator's amplitude goes zero.
