How Forced Oscillation Leads to Resonance: Key Principles & Applications
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.
FAQs on Forced Oscillation and Resonance in Physics
1. What is meant by a forced oscillation in Physics?
A forced oscillation occurs when an external, periodic force is continuously applied to an oscillating system. Unlike a free oscillation which vibrates at its own natural frequency, a body undergoing forced oscillation is compelled to vibrate at the frequency of the external force (also known as the driving frequency). An everyday example is periodically pushing a child on a swing to keep it moving.
2. What is resonance in the context of oscillations?
Resonance is a special case of forced oscillation. It is the phenomenon where the frequency of the applied external force becomes equal to the natural frequency of the oscillating system. When this occurs, the system absorbs maximum energy from the external source, causing the amplitude of the oscillation to increase dramatically. A system vibrating under this condition is said to be in resonance.
3. What is the key difference between forced oscillation and resonance?
The key difference lies in the relationship between the driving frequency and the natural frequency. Forced oscillation is the general phenomenon where an object is made to oscillate by any external periodic force, regardless of its frequency. Resonance is a specific, high-amplitude outcome that happens only when the driving frequency precisely matches the system's natural frequency.
4. Can you provide some real-life examples of resonance?
Resonance is observed in many real-world situations. Some common examples include:
Tuning a Radio: When you turn the knob of a radio, you are changing the natural frequency of its electrical circuit. When this frequency matches the frequency of a particular radio station (the driving frequency), resonance occurs, and you hear that station clearly.
Microwave Ovens: Microwaves generate radiation at a frequency that matches the natural frequency of water molecules. This causes the water molecules in food to resonate, rapidly increasing their energy and heating the food.
Musical Instruments: The body of an acoustic guitar resonates with the vibrations of the strings, amplifying the sound.
5. How does damping affect resonance?
Damping, which is the presence of resistive forces like friction or air resistance, has a significant impact on resonance. It reduces the amplitude of the oscillations at resonance. In a system with very low damping, the resonant amplitude can become extremely large, which can be destructive. In a system with high damping, the resonant peak is much lower and broader. Therefore, damping is crucial in controlling the response of a system at its resonant frequency.
6. What is the condition for resonance to occur?
The fundamental condition for resonance to occur in a system is straightforward: the frequency of the external driving force (f_d) must be equal to the natural frequency of oscillation (f_n) of the system. At this point, the energy transfer from the driver to the system is at its maximum efficiency.
7. Why are soldiers advised to break step while crossing a suspension bridge?
This is a classic precaution to avoid resonance. The rhythmic marching of soldiers acts as a periodic external force on the bridge. If the frequency of their steps happens to match the natural frequency of the bridge, resonance can occur. This would cause the bridge to oscillate with dangerously large amplitudes, potentially leading to structural failure and collapse. By breaking step, the soldiers apply an irregular, non-periodic force, preventing resonance.
8. How are free, damped, and forced oscillations related to each other?
These three types of oscillations describe the behaviour of a system under different conditions:
Free Oscillation: An ideal oscillation where a system vibrates at its natural frequency without any damping or external force.
Damped Oscillation: A realistic oscillation where resistive forces (damping) cause the amplitude to decrease over time until it stops.
Forced Oscillation: This occurs when an external periodic force is applied to a damped system to counteract the energy loss and maintain the oscillation. Resonance is the maximum possible response of such a forced system.
