What is Oscillation?
The repeated back and forth movement between two positions or states of an object is known as oscillation. It can also be referred to as the periodic motion that has the tendency to repeat itself in a regular cycle. For example- a sine wave, with a side-to-side pendulum swing, or the up-down motion with a weight of a spring. The oscillating movement takes place around an equilibrium point or a mean value. This motion is also referred to as the periodic motion. A single oscillation is considered to be a completed movement over a period of time whether it is a side to side movement or an up-down movement.
The motion of the body is said to be oscillatory or vibratory motion if it moves back and forth (to and fro) about a fixed position or point after a regular interval of time. The fixed point about which the body oscillates is called mean position and equilibrium position. Every oscillatory motion is periodic but every periodic motion is not oscillatory. Some of the examples of oscillatory motion are Vibration of wire of sitar and oscillation of the mass suspended from spring.
Oscillation- Examples
The tides in the sea and the movement of a simple pendulum of the clock are some of the most common examples of oscillations. The vibrations caused by the guitar strings and the other instruments having strings are also examples of oscillations. The movements caused by oscillations are referred to as oscillating movements. For example, oscillating movements in a sine wave or a spring when it moves up and down.
In Oscillating movements, the maximum distance covered or the height in which the oscillations take place is known as the amplitude. In order to complete one complete cycle the time taken is known as the time period of the oscillation. The number of oscillating cycles completed in one second is referred to as the frequency which is the reciprocal of the time period.
\[Frequency = \frac{1}{Time}\]
Simple Pendulum
If a heavy point mass is suspended by a weightless, inextensible, and perfectly flexible string from rigid support then this arrangement is called a simple pendulum.
Expression for time period:
For an angular momentum, sin θ, so that
F = -mgsin θ
= -mgθ
= -( mg/l )y = -Ky
Because Y = lθ, thus the time period of the simple pendulum is: T=2π√L/g. This equation is valid only when the length of a simple pendulum (l) is negligible as compared to the radius of the earth.
If a simple pendulum of density rho is made to oscillate in a liquid of density rho then its time period will increase as compared to that of air and is given by:
\[T = \frac{2\pi \sqrt{L}}{1-(\frac{{\sigma }}{\rho})}\]
If the bob of a simple pendulum has positive charge q and the pendulum is placed in a uniform electric field E which is in a vertically downward direction then the time period decreases.
\[T = \frac{2\pi \sqrt{L}}{g} + \frac{qe}{m}\]
Compound Pendulum
Any rigid body which is free to oscillate in a vertical plane about a horizontal axis passing through a point is defined as a compound pendulum
Oscillation- Types
Oscillation can be classified into the following types which are as follows-
Free Oscillation
When the body, in an oscillating movement, vibrates with a frequency of its own, the oscillation is known as free oscillation. It has a constant amplitude and period to set the oscillation without any external force. Examples of free oscillation include the vibrations caused by a tuning fork.
Damped Oscillation
Most of the free oscillations, due to the ever-present damping forces in the surrounding, eventually die out. The type of oscillation that is decreased with time is known as damped oscillation. The damping is caused due to external factors which include friction or air resistance which further reduces the amplitude of the oscillation with time and this results in the loss of energy in the system. Examples of damped oscillation include decaying oscillations of a pendulum.
Forced Oscillation
When an external period force influences something to oscillate it is known as forced oscillation. In this case, the amplitude experiences damping but due to external energy supplied to it, it remains constant. Examples of forced oscillation include feet moved by a child in order to move the swing.
When the frequency of a driving system is equal to its natural frequency then the phenomenon is known as resonance. The amplitude of the forced oscillations is higher as the damping of the system is less near resonance. A broader reaction is received to drive various frequencies as more damping is there.
Resonance
When the frequency of external force (driver) is equal to the natural frequency of the oscillator (driven), then this state of driven and driven is known as the state of resonance. In the state of resonance there occurs maximum transfer of energy from driven to the driver. Hence the amplitude of motion becomes maximum. In the state of the resonance frequency of the driver is known as the resonant frequency.
Coupled Oscillation
A system of two or more oscillations linked together in such a way that there is a mutual exchange of energy between them is called a coupled system. The oscillations of such a system are called coupled oscillations. The examples of coupled systems are as under:
Two masses are attached to each other by three springs between two rigid supports. The middle spring can be viewed as a coupling between the driven system and the driving system.
Two simple pendulums hang from the same rigid support with their bobs attached to each other by a spring.
FAQs on Oscillation
1. What is oscillation in Physics?
In Physics, an oscillation refers to the repeated to-and-fro or back-and-forth movement of an object about a central, stable position called the equilibrium position. This movement is also known as vibratory motion. A key characteristic is that it is a type of periodic motion, meaning it repeats itself in regular time intervals.
2. What are some common examples of oscillatory motion?
Oscillatory motion is observed in many everyday phenomena. Common examples include:
- The swinging of a pendulum in a clock.
- The up-and-down movement of a mass attached to a spring.
- The vibration of a guitar string after being plucked.
- The movement of a tuning fork.
- The bouncing of a ball around its point of rest.
3. How is oscillatory motion different from periodic motion?
While related, they are not the same. The key difference lies in the nature of the movement. Periodic motion is any motion that repeats itself after a fixed interval of time, like the Earth revolving around the Sun. Oscillatory motion is a specific type of periodic motion where the object moves back and forth about a fixed equilibrium point. Therefore, all oscillatory motions are periodic, but not all periodic motions are oscillatory.
4. What is Simple Harmonic Motion (SHM) and why is it considered a special type of oscillation?
Simple Harmonic Motion (SHM) is the most fundamental type of oscillatory motion. It is considered special because the restoring force acting on the object is directly proportional to its displacement from the equilibrium position and always acts in the opposite direction of the displacement (F ∝ -x). This unique condition makes its motion describable by simple sine and cosine functions, forming the basis for analysing more complex oscillations.
5. What are the key parameters used to describe an oscillation?
An oscillation is described by three main parameters:
- Amplitude (A): The maximum displacement of the object from its equilibrium position.
- Time Period (T): The time taken to complete one full oscillation.
- Frequency (f): The number of complete oscillations that occur per unit of time. It is the reciprocal of the time period (f = 1/T).
6. What are the main types of oscillations?
Oscillations can be broadly classified based on the forces acting on the system:
- Free Oscillation: Occurs when an object vibrates with its own natural frequency without any external force after being displaced initially.
- Damped Oscillation: Occurs when resistive forces (like friction or air resistance) cause the amplitude of the oscillation to decrease over time, eventually stopping the motion.
- Forced Oscillation: Occurs when a continuous external periodic force is applied to an oscillating body, causing it to vibrate with the frequency of the external force.
7. What is the physical significance of resonance in forced oscillations?
Resonance is a critical phenomenon in forced oscillations that occurs when the frequency of the applied external force matches the natural frequency of the oscillating system. Its physical significance is that at this specific frequency, the system absorbs maximum energy from the external source, leading to a dramatic increase in the amplitude of the oscillations. This principle is used in applications like tuning a radio but can also be destructive, as seen in the collapse of bridges due to resonant vibrations.
8. Is the motion of a simple pendulum always Simple Harmonic Motion? Explain the conditions.
No, the motion of a simple pendulum is not always a perfect Simple Harmonic Motion. It is only an approximation of SHM under a specific condition: the amplitude of the swing must be very small. For small angles (typically less than 10 degrees), the restoring force is approximately proportional to the displacement (sin θ ≈ θ). If the angle of swing is large, this approximation is no longer valid, and the motion becomes oscillatory but not simple harmonic.
9. What is the formula for the time period of a simple pendulum?
As per the CBSE 2025-26 syllabus, the formula for the time period (T) of a simple pendulum, under the condition of small angular displacement, is:
T = 2π√(L/g)
Where:
- T is the time period.
- L is the effective length of the pendulum.
- g is the acceleration due to gravity.
This formula shows that the time period depends only on the pendulum's length and gravity, not on its mass or amplitude (for small swings).
10. How do damping forces affect real-world oscillatory systems like a swing?
In a real-world system like a playground swing, damping forces such as air resistance and friction at the pivot point continuously oppose the motion. This causes the swing's energy to dissipate, primarily as heat. As a result, the amplitude of the swing (how high it goes) gradually decreases with each pass. To keep swinging, a person must apply an external periodic force (by pumping their legs) to counteract the energy loss due to damping. This is an example of moving from a damped oscillation to a forced oscillation.
