Forced Oscillation and Resonance

What is Forced Oscillation?

Have you ever wondered how radio plays a channel of a selected frequency or why the voice of an opera singer shatters a wine glass? Well, it all happens due to the phenomenon of forced oscillation and resonance. Under normal conditions, when there is no external damping or driving force, a system will generally oscillate at its natural frequency. But, when a driving force is applied to the system periodically, some energy is put into the system at a frequency different from the system's natural frequency of oscillation. The system will now be "forced" to vibrate with the frequency of the external periodic force, giving rise to forced oscillations. The difference between the natural frequency of the system and that of the driving force will determine the amplitude of the forced vibrations; a larger frequency difference will result in a smaller amplitude.

How Are Free and Forced Oscillations Different?

Free oscillations differ from forced oscillations in the following respects:

  • Free oscillations or vibrations occur in the absence of an external force. But forced oscillations take place under the influence of an external driving force.

  • While the frequency of free oscillations depends solely on the source of vibrations, the frequency of forced oscillations is affected by the source of vibration and the frequency of the applied driving force.

  • In the case of free oscillations, the frequency of vibration remains constant throughout. However, the frequency of forced oscillations can be altered by changing the frequency of the driving force.

  • The amplitude of the vibrations remains constant for free oscillations. But in the case of forced oscillations, the amplitude may increase, decrease, or remain constant.

What is Resonance? 

So what gives rise to resonance oscillation? Resonance is a particular case of forced oscillation. When the frequency difference between the system and that of the external force is minimal, the resultant amplitude of the forced oscillations will be enormous. However, when the two frequencies match or become the same, resonance occurs. Thus, at resonance, the amplitude of forced oscillation is maximal, and the natural oscillating frequency of the system is equal to the frequency of the periodic driving force. 

The following diagram illustrates forced oscillations and resonance:

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Displacement-Time Graphs for Different Oscillations

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Types of Resonance

Resonance can be of the following types:

  • Mechanical Resonance: A mechanical system tends to absorb more energy when the natural frequency of vibration of the system matches the frequency of its oscillations. The phenomenon of mechanical resonance may result in extreme vibrations leading to wild swaying motions and often, the collapse of structures like buildings, bridges, trains, and aircraft.

  • Acoustic Resonance: The mechanical vibrations that occur in the audible range of the human ear constitute acoustic resonance. It is a branch of mechanical resonance that deals with the vibrations produced within the frequency range of 20 Hz to 20 kHz. Acoustic resonance is a crucial factor for building instruments that use resonators, like the body and strings of a violin, the length of a flute tube, or the tension of a drum membrane.

  • Electrical Resonance: The phenomenon of electrical resonance is observed in electrical circuits. It is used to transmit and receive wireless communication as in cell phones, television, and radio.

  • Optical Resonance: Optical resonators or a resonant optical cavity is widely used in lasers. It comprises an arrangement of optical components that enables the circulation of a beam of light in a closed path. 

  • Orbital Resonance: This is a concept related to celestial mechanics. In the case of orbital resonance, two orbiting bodies mutually exert a periodic and regular gravitational force. As a result, the mutual gravitational effect of the bodies is greatly enhanced.

  • Atomic Resonance: The concept of resonance in particle physics pertains to particular quantum mechanical properties observed in an atomic nucleus under the influence of an externally applied magnetic field. Nuclear Magnetic Resonance (NMR) finds application in several scientific techniques like spectroscopy and Magnetic Resonance Imaging (MRI); NMR spectroscopy can be used to study molecules, crystals, and non-crystals, whereas MRI is used in medical imaging procedures.

FAQ (Frequently Asked Questions)

1. What are the Different Types of Oscillations?

  • Free oscillations: A body is said to perform free oscillations when it vibrates with its natural frequency. Example: Vibrations of a stretched string.

  • Damped oscillations: During oscillation, a damping force arises due to air resistance or friction offered by the medium. As a result, the amplitude of such oscillations decreases with time and eventually becomes zero. Example: swings of a pendulum.

  • Maintained oscillations: If some energy is fed to a system, the amplitude of oscillations can be kept constant. The supplied energy compensates for the energy lost due to damping forces and gives rise to maintained oscillations. Example: a swing to which constant energy is provided.

  • Forced oscillations: When a vibrating body is acted upon by a force of frequency different from the body's natural frequency, the body is said to undergo forced oscillations. Example: sound-box of stringed instruments. 

2. What are Some Real-life Examples of Resonance?

  • Swings: A swing's motion is built by giving it a series of regular pushes. When the pusher syncs with the swing's timing, the swing oscillates with increased amplitude and goes higher. At its natural frequency of oscillation, even a gentle push will maintain its amplitude due to resonance.

  • Guitar: In acoustic guitars, a plucked string vibrates and relays the sound energy to the sound-box. The air inside the sound-box resonates and amplifies the sound, making it louder.

  • Opera singers: If the frequency of a singer's voice matches the resonant frequency of a glass object, a transfer of energy occurs, causing the glass to shatter.

  • Bridge: A group of soldiers marching on a bridge is asked to break steps. If the frequency of their synchronized marching matches the natural frequency of the bridge, the bridge can collapse due to extreme vibrations.