What are Oscillations?
Many motions in nature repeat themselves — the swinging of a pendulum, the vibration of a guitar string, or the alternating current in an electrical circuit. These repeated to-and-fro motions are called Oscillations. When such oscillations travel through space or a medium, they form Waves.
Definition of an Oscillation
An Oscillation is a periodic back-and-forth motion (also called Vibratory motion) of an object about a fixed equilibrium position.
- The object moves alternately to either side of the mean position.
- Each complete to-and-fro motion is called one cycle.
- The number of cycles per second is the frequency (f), measured in hertz (Hz).
- The time period (T) is the time taken to complete one cycle.
T = 1⁄f
Motion of a pendulum showing amplitude, mean position, and extreme positions.
Simple Harmonic Motion (SHM)
The simplest and most important type of oscillatory motion is Simple Harmonic Motion.
In SHM, the restoring force is directly proportional to the displacement and acts in the opposite direction:
F=−kx
- Displacement: x = Asin(ωt+ϕ)
- Velocity: v = ωAcos(ωt+ϕ)
- Acceleration: a = −ω2x
- Energy: E = 1⁄2 kA2 (constant)
Graph showing how displacement, velocity, and acceleration vary with time
Characteristics of Simple Harmonic Motion (SHM)
| Quantity | Symbol | Unit | Description |
|---|
| Amplitude | A | m | Maximum displacement |
| Time Period | T | s | Time for one cycle |
| Frequency | f | Hz | Number of cycles per second |
| Angular frequency | ω | rad/s | ω = 2πf = 2π⁄T |
Energy in Simple Harmonic Motion (SHM)
Energy in a Simple Harmonic Motion (SHM) system oscillates between kinetic and potential forms.
| Position | Kinetic Energy | Potential Energy |
|---|---|---|
| Mean | Maximum | Zero |
| Extreme | Zero | Maximum |
Total Mechanical energy remains constant.
Examples of Oscillatory Motion
Examples of Oscillatory Motion are:
Pendulum Clock: The swinging pendulum in a clock. It moves back and forth around its equilibrium position, driven by gravity and inertia.
Mass-Spring System: A weight attached to a spring oscillates up and down when displaced. This is a fundamental model used in physics to study harmonic motion.
Tuning Fork: When struck, the prongs of a tuning fork vibrate rapidly, producing sound waves. This is oscillatory motion in a solid system.
Swing: A child’s swing moves back and forth due to gravitational restoring force, making it a simple real-life oscillatory system.
Flapping of Bird Wings: The repetitive up-and-down motion of wings during a bird’s flight is oscillatory in nature.
Musical Instruments (Strings): Guitar or violin strings vibrate when plucked, producing oscillations that generate sound.
Alternating Current (AC): Electrical current in AC circuits oscillates periodically, changing direction and magnitude over time.
Beating of the Heart: The rhythmic contraction and relaxation of the heart muscles is a biological oscillatory system.
Earthquake Vibrations: Seismic waves generated during earthquakes are oscillatory motions traveling through Earth’s crust.
Damped Oscillations
In real life, oscillations gradually lose energy due to friction or resistance.
Such oscillations whose amplitude decreases with time are damped oscillations.
Damped oscillation curve showing amplitude decay
Equation:
x = Ae−βt sin(ωt+ϕ)
where β is the damping constant.
Real-life Examples of Damped Oscillations
1. A Pendulum in Air
A swinging pendulum in air experiences air resistance and friction at its pivot.
- Its swings become smaller and smaller until it stops completely.
- The amplitude decreases exponentially with time.
2. Car Shock Absorber
The shock absorber in a car’s suspension system is a practical damped oscillator.
- It prevents the car from bouncing continuously after hitting a bump.
- Hydraulic damping converts vibrational energy into heat.
3. Tuning Fork in Air
When a tuning fork vibrates,
- The surrounding air exerts resistance.
- The fork gradually stops vibrating as its amplitude decays.
4. Spring–Mass System in Oil or Water
When a Spring–Mass system is immersed in a viscous liquid (like oil),
- The liquid’s resistance damps the oscillations.
- The system still oscillates, but the amplitude decays quickly.
Forced Oscillations
When an external periodic force continuously drives a system, the system performs forced oscillations.
In such cases, the system oscillates with the frequency of the applied force, and not in its own natural frequency.
Examples:
1. Tuning Fork Mounted on a Resonance Box
When a tuning fork is struck, its prongs vibrate and drive the air column in the attached wooden box.
The air molecules inside are forced to oscillate with the same frequency as the tuning fork, and that is a forced oscillation.
2. Car Engine Vibrations
When an automobile engine runs, the vibration of the engine forces the car body to oscillate. The car body itself has a natural frequency. When the engine’s frequency matches or nears it, large vibrations occur, known as resonance (see next section on Resonance). To prevent damage, engineers use damping and insulation systems.
3. Loudspeaker Cone
The cone of a loudspeaker vibrates under the influence of an alternating current supplied by the audio amplifier. The frequency of vibration of the cone (and hence sound) equals the frequency of the electrical signal.
4. Building Shaken by Earthquake Tremors
During an earthquake, ground vibrations act as external periodic forces on tall buildings. These structures oscillate at the frequency of the tremors, which can lead to resonance if the frequencies match. That’s why modern buildings are designed with damping systems to reduce resonance.
Examples of Forced Oscillations
Resonance
Resonance occurs when the frequency of the external force matches the natural frequency of the system — leading to a large amplitude of oscillation.
Examples:
- Glass shattering at a particular sound frequency
- Bridge vibrations (e.g., Tacoma Narrows Bridge)
- Tuning a radio to a desired station frequency
Resonance curve showing amplitude vs frequency
From Oscillations to Waves
When oscillations of one particle set neighboring particles into motion, the disturbance travels through the medium — forming a wave.
Hence, wave motion is the transmission of oscillations through space or a medium.
Oscillations transferring from particle to particle in a wave
Types of Waves:
- Mechanical Waves: Require a medium (sound, water waves).
- Electromagnetic Waves: Do not need a medium (light, radio waves).
- Transverse Waves: Particle motion ⟂ direction of wave propagation.
- Longitudinal Waves: Particle motion ∥ direction of wave propagation.
Next Topic (Coming Soon)
Read next: Waves – The Motion of Energy Through Matter and Space