"In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position."
The motion of an object back and forth around a central or equilibrium position, where the acceleration is proportional to the displacement from the equilibrium position, also known as simple harmonic motion.
Simple Harmonic Motion: It is the motion of an object that moves back and forth over a fixed path with a restoring force proportional to the displacement from the equilibrium position.
Damped Harmonic Motion: It is the motion of an object that gradually loses energy due to friction or other forms of resistance.
Forced Harmonic Motion: It is the motion of an object that is acted upon by an external periodic force, causing the object to vibrate with the same frequency as the external force.
Resonance: It is the phenomenon in which an object vibrates at its natural frequency in response to an external force of the same frequency, resulting in a dramatic increase in amplitude.
Waves: They are disturbances that propagate through a medium or space, transporting energy without transporting matter.
Transverse Waves: They are waves in which the particles of the medium vibrate perpendicular to the direction of wave propagation.
Longitudinal Waves: They are waves in which the particles of the medium vibrate parallel to the direction of wave propagation.
Wave Properties: These include amplitude, frequency, wavelength, wave speed, and phase.
Wave Interference: It is the phenomenon in which two or more waves interact with each other, resulting in either constructive or destructive interference.
Doppler Effect: It is the change in frequency or wavelength of a wave due to the motion of the source or the observer.
Standing Waves: They are waves that do not appear to propagate through the medium but instead oscillate in place, resulting in a pattern of nodes and antinodes.
Properties of Sound: These include frequency, amplitude, speed, intensity, and wavelength.
Beats: They are the periodic variation in amplitude or loudness that results from the interference of two sound waves of slightly different frequencies.
Musical Instruments: They produce sound through the vibration of a physical element (such as a string or a column of air) to create harmonic frequencies.
Electromagnetic Waves: They are waves that propagate through a medium or space by the mutual interaction of electric and magnetic fields.
Polarisation: It is the phenomenon in which the direction of the electric field in an electromagnetic wave is fixed, resulting in the transverse wave oscillating in only one direction.
Reflection, Refraction, and Diffraction: These are the ways in which electromagnetic waves interact with boundaries and obstacles in their path.
Applications of Waves and Oscillations: These include medicine, engineering, telecommunications, and physics research.
Simple Harmonic Motion: It is the most fundamental and basic type of harmonic motion where the restoring force is directly proportional to the displacement from the equilibrium position and the motion follows a sine or cosine curve.
Damped Harmonic Motion: In this type of harmonic motion, the amplitude of oscillation gradually decreases over time due to the presence of a damping force such as friction or air resistance.
Forced Harmonic Motion: When an external force is applied to a system undergoing simple harmonic motion, it causes the motion to deviate from its natural frequency and follow the frequency of the applied force.
Parametric Oscillation: In this type of harmonic motion, the frequency of oscillation changes periodically due to variations in the properties of the system such as its mass, length, or stiffness.
Nonlinear Oscillation: When the restoring force acting on a system is not directly proportional to the displacement, it produces a nonlinear oscillation where the motion follows a more complex curve than a simple sine wave.
Standing Waves: When two waves of the same frequency and amplitude traveling in opposite directions collide, they create a pattern of nodes (points of zero displacement) and antinodes (points of maximum displacement) that do not move with time.
Transverse Waves: In a transverse wave, the direction of wave propagation is perpendicular to the direction of oscillation of the individual particles of the medium through which it travels.
Longitudinal Waves: In a longitudinal wave, the direction of wave propagation is parallel to the direction of oscillation of the individual particles of the medium through which it travels.
Surface Waves: Surface waves are a combination of transverse and longitudinal waves that occur at the interface between two media of different densities, such as water and air.
Electromagnetic Waves: Electromagnetic waves are waves that propagate through space without the need for a medium and are characterized by their varying electric and magnetic fields.
"[...] a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position."
"It results in an oscillation that is described by a sinusoid which continues indefinitely."
"Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law."
"[...] when it is subject to the linear elastic restoring force given by Hooke's law."
"The motion is sinusoidal in time and demonstrates a single resonant frequency."
"Yes, other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum."
"[...] the net force on the object at the end of the pendulum must be proportional to the displacement."
"[...] it is only a good approximation when the angle of the swing is small; see small-angle approximation."
"Simple harmonic motion can also be used to model molecular vibration."
"Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis."
"[...] whose magnitude is directly proportional to the distance of the object from an equilibrium position."
"It results in an oscillation that is described by a sinusoid which continues indefinitely (if uninhibited by friction or any other dissipation of energy)."
"[...] a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position."
"Simple harmonic motion can serve as a mathematical model for a variety of motions."
"The motion is sinusoidal in time and demonstrates a single resonant frequency."
"[...] the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law."
"Simple harmonic motion can serve as a mathematical model for a variety of motions."
"It is only a good approximation when the angle of the swing is small; see small-angle approximation."
"Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis."