oscillating

Examples of oscillating in the following topics:

• Driven Oscillations and Resonance

  • Driven harmonic oscillators are damped oscillators further affected by an externally applied force.
  • If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator.
  • Driven harmonic oscillators are damped oscillators further affected by an externally applied force F(t).
  • The time an oscillator needs to adapt to changed external conditions is of the order τ = 1/(ζ0).
  • Describe a driven harmonic oscillator as a type of damped oscillator

• Applications of Second-Order Differential Equations

  • In this atom, we will learn about the harmonic oscillator, which is one of the simplest yet most important mechanical system in physics.
  • If $F$ is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency.
  • In real oscillators, friction (or damping) slows the motion of the system.
  • Driven harmonic oscillator: Driven harmonic oscillators are damped oscillators further affected by an externally applied force $F(t)$.
  • A solution of damped harmonic oscillator.

• Forced Vibrations and Resonance

  • In this example, he or she is causing a forced oscillation (or vibration).
  • After driving the ball at its natural frequency, the ball's oscillations increase in amplitude with each oscillation for as long as it is driven.
  • In real life, most oscillators have damping present in the system.
  • These features of driven harmonic oscillators apply to a huge variety of systems.
  • Heavy cross winds drove the bridge into oscillations at its resonant frequency.

• The Production of Electromagnetic Waves

  • As it travels through space it behaves like a wave, and has an oscillating electric field component and an oscillating magnetic field.
  • These waves oscillate perpendicularly to and in phase with one another.
  • When it accelerates as part of an oscillatory motion, the charged particle creates ripples, or oscillations, in its electric field, and also produces a magnetic field (as predicted by Maxwell's equations).
  • This means that an electric field that oscillates as a function of time will produce a magnetic field, and a magnetic field that changes as a function of time will produce an electric field.
  • Electromagnetic waves are a self-propagating transverse wave of oscillating electric and magnetic fields.

• Longitudinal Waves

  • Longitudinal waves, sometimes called compression waves, oscillate in the direction of propagation.
  • The difference is that each particle which makes up the medium through which a longitudinal wave propagates oscillates along the axis of propagation.
  • In the example of the Slinky, each coil will oscillate at a point but will not travel the length of the Slinky.
  • Matter in the medium is periodically displaced by a sound wave, and thus oscillates.
  • The wave propagates in the same direction of oscillation.

• Oscillator Strengths

  • A classical harmonic oscillator driven by electromagnetic radiation has a cross-section to absorb radiation of
  • Except for the degeneracy factors for the two states, the Einstein coefficients will be the same, so we can define an oscillator strength for stimulated emission as well,
  • There are several summation rules that restrict the values of the oscillator strengths,
  • We can also separate the emission from absorption oscillator strengths

• Energy in a Simple Harmonic Oscillator

  • The total energy in a simple harmonic oscillator is the constant sum of the potential and kinetic energies.
  • In the case of undamped, simple harmonic motion, the energy oscillates back and forth between kinetic and potential, going completely from one to the other as the system oscillates.
  • A known mass is hung from a spring of known spring constant and allowed to oscillate.
  • The time for one oscillation (period) is measured.
  • Explain why the total energy of the harmonic oscillator is constant

• Waves

  • In nature, oscillations are found everywhere.
  • From the jiggling of atoms to the large oscillations of sea waves, we find examples of vibrations in almost every physical system.
  • They consist, instead, of oscillations or vibrations around almost fixed locations.
  • A wave can be transverse or longitudinal depending on the direction of its oscillation.
  • Longitudinal waves occur when the oscillations are parallel to the direction of propagation.

• Transverse Waves

  • If a transverse wave is moving in the positive x-direction, its oscillations are in up and down directions that lie in the y–z plane.
  • Transverse waves are waves that are oscillating perpendicularly to the direction of propagation.
  • Here we observe that the wave is moving in t and oscillating in the x-y plane.
  • A wave can be thought as comprising many particles (as seen in the figure) which oscillate up and down.
  • As time passes the oscillations are separated by units of time.

• Forced motion

  • The forcing function doesn't know anything about the natural frequency of the system and there is no reason why the forced oscillation of the mass will occur at $\omega_0$ .
  • The motion of the mass with no applied force is an example of a free oscillation.
  • Otherwise the oscillations are forced.
  • An important example of a free oscillation is the motion of the entire earth after a great earthquake.
  • Free oscillations are also called transients since for any real system in the absence of a forcing term, the damping will cause the motion to die out.