Forced Oscillation And Resonance

Did you know that squad of soldiers is asked not to march across a bridge, but always to run haphazardly? To put it in simple terms, if they were to march across as a parade, their frequency may match with the natural frequency of the bridge in consideration causing it to fall, prove dangerous for the people around it.

The natural frequency is the frequency at which a system oscillates when not subjected to any external influences. Have you ever seen someone tune a guitar? They either use a tuner or another guitar such that the frequency of the string in consideration matches with the gauge.

The above instances are examples of resonance. In the first case, the frequency of soldier’s march is considered to be in resonance with that of the natural frequency of the bridge to cause failure. A similar phenomenon is presented in the second case.

What is Resonance?

When an external vibrating system causes another system to oscillate with greater amplitude at a specific frequency, the phenomenon is called resonance, and that specific frequency is called resonant frequency.

The bridge mentioned in the first instance may fail due to this oscillation at great amplitude. While tuning a guitar (one system) using another guitar (another system), you can see that at the resonant frequency, the amplitude of vibration of the string is greatest.

These large amplitude oscillations produced at the resonant frequencies are because of vibrational energy being stored in the system.

Types of Resonance

  • Mechanical  (in bridges)
  • Acoustic  (in instruments)
  • Orbital (orbiting bodies influencing each other)
  • Electrical  (in electrical circuits)
  • Particle (atoms, molecules and other such particles influencing each other) and
  • Optical Resonance (light waves influencing each other)

Practise This Question

Suppose the amplitude of a forced oscillator is given as  xm=Fm[m2(ω2dω2)+b2ω2d]12 where Fm is the (constant) amplitude of the external oscillating force. At resonance,

what are the amplitude and velocity amplitude of the oscillating object?