Concept of Resonance and its Characteristics

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

When pendulum A is displaced, it oscillates with a natural frequency, and the energy from pendulum A is transferred to the other pendulums, forcing them to oscillate with a driving frequency.

The given expression relates the amplitude with natural and driving frequency.

On close observation, it is found that pendulums B and D oscillate with driving frequencies quite different from their natural frequencies, resulting in smaller amplitudes.

In contrast, the driving frequency of the pendulums with identical lengths is equal to their natural frequency, causing the amplitude to increase gradually with each oscillation. This condition—when the driving frequency equals the natural frequency—is called resonance.

In a damped harmonic oscillator, under the resonance condition, the amplitude can be altered depending on the damping force. The amplitude is large and narrow for small damping, while it is smaller for heavy damping.