In this section, we will define oscillating motion which comes under the type of periodic movements. You will also come across detailed explanations on concepts like how to find period of oscillation, simple harmonic motion, and different types of oscillatory motions, which will help you gain a better understanding of the subject.
In our daily lives, we come across several such incidents that involve repetitive movements of objects. Be it the movement of your bicycle wheels, a football’s motion as you kick it, or strings of a playing guitar. If you observe closely, a lot of these movements take place in a rhythm while others do not. The former are grouped as periodic motions while the latter are categorized as non-periodic motions.
In Physics, the definition of oscillation is put forth as a periodic variation in time of a matter about its mean value or between two fixed states.
One complete cycle of periodic to and fro motion of a body about its central position serves to define one oscillation.
There are several frequently observed motions that serve as examples of oscillation. The most popular one out of them is the motion of a pendulum bob. It is a repetitive motion with the bob rising to its right, coming back to its center position, again rising to its left, and finally going back to its center again. This total cycle constitutes 1 oscillation. Additional examples include movements of elastic media and springs.
Several measurements define oscillation. Here, we have explained each parameter with their respective unit of measure and the formulae to calculate their value and also understand how to define oscillating motion.
Period of Oscillation
The time taken by an oscillating body to complete one cycle of motion is termed as its oscillation period. It is generally measured in second and is denoted by T.
Here’s how to calculate period of oscillation.
T = 2π √(L/g)
Where L represents the length of a pendulum and g is the acceleration due to gravity.
Frequency of Oscillation
The number of oscillations a body can complete in one second is known as its frequency of oscillation. It is primarily expressed in the SI unit of Hertz and is denoted by the letter f.
You can calculate the value of f with its relation to period T of oscillation as follows:
f = 1/T
Amplitude of Oscillation
The maximum amount of displacement of an oscillating body from its central position is known as its amplitude. Its value is measured in meter and it is denoted by A.
With a known value of A, displacement x is calculated as -
x = A cos 2πft
Where t denotes the time for which oscillation is taking place.
Simple harmonic motion (SMH) is defined as a periodic oscillation of an unaltering frequency and a constant amplitude where the magnitude of restoring force on the object is always acting towards its equilibrium position and is directly proportional to its displacement.
Simple harmonic motion is the simplest form of oscillatory motion meaning. It is an ideal condition where the maximum displacement on one side of the equilibrium position is exactly equal to that on the other side. This aspect is also required to define oscillating motion.
SHM is denoted by y, and its mathematical expression is -
y = A sin ωT or A cos ωT
Where A stands for amplitude, ω stands for angular frequency, and T stands for time.
A perfect example of the simple harmonic motion is again motion of a simple pendulum because, on its displacement in one direction, a proportional restoring force acts on it in the opposite direction.
Based on the external forces acting on them, simple harmonic motions are classified into three significant categories. Now we will define oscillating motion and its types with a brief description of each.
A free oscillation is an ideal condition where a particle’s motion is not under the influence of any external resistance. It is a motion with a natural frequency of the particle and constant amplitude, energy, and period.
It is an ideal condition because, in reality, every oscillating object undergoes some form of interaction with external conditions resulting in loss of energy. An example of free oscillations is the motion of a simple pendulum in a vacuum.
A damping oscillation is one in which the moving particle gradually loses its kinetic energy on interaction with resistive forces like air or friction. Due to this resistance offered by external forces, the displacement of a particle slowly reduces with time and ultimately reaches its state of rest. A simple oscillating pendulum under natural conditions is an excellent example of damped oscillations.
Forced oscillations in a particle are a result of a continuous application of external force to help it maintain a motion of constant amplitude, time, and frequency. In these cases, the damping forces are canceled out with the help of artificial external conditions so that a periodic motion is sustained. A movement embodying forced oscillations definition is vibrations in a loudspeaker induced with the current.
The concept of Free Forced Damped Oscillations constitutes a significant portion of Class 11 Physics. It makes up almost 14% of the syllabus with some key concepts essential for competitive exams.
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1. What is the angular frequency of Oscillatory Motion? State its SI unit and mathematical expression.
Ans. Angular frequency is defined as the frequency of a periodic rotational motion and is equivalent to the frequency of rotational cycles multiplied with factor 2π. It is denoted by the Greek letter ω (small omega).
In the SI unit, angular frequency is measured in radians per second (rad s-1), and it is mathematically expressed as:
ω = 2πf,
Where f stands for the frequency of oscillation.
2. What is a Multivibrator? How is it different from an Oscillator?
Ans. The simplest multivibrator definition is it is an electronic circuit with two amplifiers arranged in a way to generate oscillatory wave-forms.
An oscillator is an electronic circuit that is tuned to generate a continually flowing output of wave-form. A multivibrator circuit, on the other hand, is used to implement a wide range of simple two-state devices, such as timers, oscillators, and flip-flops.
3. What are the conditions for Simple Harmonic Motion?
Ans. Simple harmonic motion (SMH) is an ideal and most fundamental condition of oscillatory motion. There are a set of conditions it follows, which have been discussed below.
Objects must be performing back and forth or to and fro motion about a set position also called its equilibrium position.
A perfectly elastic restoring force must be acting on the whole system of motion and should be directed towards the particle’s mean position.
Acceleration of the particle must be directly proportional to its displacement from the central position.
4. At what position does the pendulum have maximum and minimum acceleration?
Ans. The acceleration of an oscillating pendulum is maximum at the highest points of its motion and is minimum, i.e., zero, at its lowest point.