[Physics Class Notes] on Forced Oscillation and Resonance Pdf for Exam

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.

Oscillation can be described as the repetitive motion of an object between two different points or states. The word Oscillation is derived from the Latin term Oscillate which means “to swing”. In simple words, when a body is in to and fro motion with respect to a central axis or point, it is termed as oscillation. You can understand the concept of oscillation very easily by observing the motion of a pendulum. The vibration of the string in instruments like the guitar is also an example of oscillation.

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 fluted 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 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.