## Oscillations – Class 11 | Chapter – 14 | Physics Short Notes Series PDF for NEET & JEE

Oscillations: Oscillations refer to repetitive, periodic motions or vibrations that occur about a central point or axis. Oscillations can be found in many natural phenomena and are used to describe a wide range of physical systems, such as the vibrations of a guitar string, the motion of a pendulum, the waves in the ocean, and the alternating current in an electrical circuit.

In physics, oscillations are often described mathematically using the concept of a wave function. This function describes the displacement of a point in space and time in response to a disturbance. The frequency of an oscillation is defined as the number of cycles of the wave function per unit of time, and its wavelength is the distance between two consecutive points in the wave with the same phase.

There are many different types of oscillations, including simple harmonic oscillations, damped oscillations, forced oscillations, and complex oscillations. Each of these types of oscillations has different characteristics and behaves differently in response to external influences. Understanding the properties of oscillations is important in fields such as engineering, physics, and biology, as they play a crucial role in a wide range of natural and man-made systems.

## Calculation of Oscillations

A simple pendulum is the most commonly used example while explaining oscillation. Hence to calculate the oscillation of a simple pendulum we can use the following formulas:

• Period of oscillation: T = 2π√L/g

Here T= Time period of oscillation

L = Length

g = Acceleration due to gravity

• Oscillation frequency: f = 1/T

Here T can be referred to as the time period of oscillation

## Types of Oscillations

There are several types of oscillations, including:

• Simple Harmonic Oscillations: This type of oscillation occurs when an object is subjected to a restoring force proportional to its displacement from an equilibrium position. This is the most basic type of oscillation and is often used as a model for other, more complex oscillations. Examples of simple harmonic oscillations include the motion of a mass on a spring and the pendulum of a clock.
• Damped Oscillations: This type of oscillation occurs when an object is subjected to a restoring force, but there is also some friction or damping that slows down the motion over time. Damped oscillations eventually come to a stop, unlike simple harmonic oscillations, which continue indefinitely.
• Forced Oscillations: This type of oscillation occurs when an object is subjected to an external periodic force, such as a wind gust or an alternating electrical current. The motion of the object is determined by the interplay between the external force and the natural frequency of the object.
• Resonant Oscillations: This type of oscillation occurs when an object is subjected to a periodic force with the same frequency as its natural frequency. The object will respond with large amplitude oscillations, and this is known as resonance.
• Complex Oscillations: This type of oscillation occurs when an object is subjected to multiple simultaneous forces with different frequencies. The result is a complex pattern of motion that can be difficult to describe mathematically. Examples of complex oscillations include the behavior of the Earth’s climate and the motion of the human heart.

Each of these types of oscillations has its own unique properties and behaviors, and understanding these properties is important in many fields, including physics, engineering, and biology.

## Oscillations Resonance

Resonance is a phenomenon that occurs when an oscillating system is subjected to a periodic external force with the same frequency as its natural frequency of oscillation. Under these conditions, the system will respond with large amplitude oscillations, which is known as resonance.

The natural frequency of an oscillating system is determined by its physical characteristics, such as mass and stiffness. When an external force with the same frequency is applied, it drives the system and amplifies its motion. The result is a resonant response that can be much larger than the original oscillations.

Resonance is an important concept in many fields, including engineering, physics, and biology. For example, engineers use resonance to design structures that can resist vibrations and seismic forces. In physics, resonance is used to explain the behavior of electric circuits and the propagation of waves in media such as air, water, and solids. In biology, resonance is important in understanding the behavior of the human body, including the mechanical properties of bones and the behavior of the human voice.

It is important to note that while resonance can enhance the motion of a system, it can also be damaging if the resonant response becomes too large. In such cases, resonant vibrations can cause structural failure or produce unwanted noise. As a result, engineers must carefully consider the potential for resonance when designing structures and systems.

There are various kinds of resonance which are as follows:

• Mechanical Resonance
• Acoustic Resonance
• Orbital Resonance
• Electrical Resonance
• Particle Resonance
• Optical Resonance

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