Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

Consider four pendulums tied to a string and suspended from a rigid support. Let the lengths of pendulum A and C be identical while pendulum B and D have different lengths.

When pendulum A is displaced, it undergoes free oscillation with a natural frequency. The natural frequency is the frequency at which the pendulum oscillates naturally...