# Antiresonance

**anti-resonanceanti-resonantantiresonatorsantiresonant**

In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase.wikipedia

48 Related Articles

### RLC circuit

**LRC circuitRLCRLC circuits**

The simplest system in which antiresonance arises is a system of coupled harmonic oscillators, for example pendula or RLC circuits.

For this reason they are often described as antiresonators, it is still usual, however, to name the frequency at which this occurs as the resonance frequency.

### Resonance

**resonantresonant frequencyresonance frequency**

In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase.

### Oscillation

**oscillatorvibrationoscillators**

In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase.

### Normal mode

**modesnormal modesmode**

:Examining these steady state solutions as a function of driving frequency, it is evident that both oscillators display resonances (peaks in amplitude accompanied by positive phase shifts) at the two normal mode frequencies.

### Tuned mass damper

**mass dampertuned mass dampersdamper**

* Antiresonance

### Physics

**physicistphysicalphysicists**

In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase.

### Amplitude

**peak-to-peakintensityvolume**

### Frequency

**frequenciesperiodperiodic**

### Phase (waves)

**phasephase shiftout of phase**

### Physical system

**systemphysical systemsphysical**

Such frequencies are known as the system's antiresonant frequencies, and at these frequencies the oscillation amplitude can drop to almost zero.

### Wave interference

**interferenceconstructive interferencedestructive interference**

Antiresonances are caused by destructive interference, for example between an external driving force and interaction with another oscillator.

### Mechanics

**mechanicaltheoretical mechanicsmechanician**

Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustic, electromagnetic and quantum systems.

### Acoustics

**acousticacousticianacoustical**

Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustic, electromagnetic and quantum systems.

### Electromagnetism

**electromagneticelectrodynamicselectromagnetic force**

Antiresonances can occur in all types of coupled oscillator systems, including mechanical, acoustic, electromagnetic and quantum systems.

### Quantum mechanics

**quantum physicsquantum mechanicalquantum theory**

### Harmonic oscillator

**harmonic oscillatorsharmonic oscillationdamped harmonic oscillator**

The simplest system in which antiresonance arises is a system of coupled harmonic oscillators, for example pendula or RLC circuits.

### Pendulum

**pendulumssimple pendulumpendula**

The simplest system in which antiresonance arises is a system of coupled harmonic oscillators, for example pendula or RLC circuits.

### Ordinary differential equation

**ordinary differential equationsordinaryODE**

The situation is described by the coupled ordinary differential equations

### Damping ratio

**dampingdampedoverdamped**

:where the \omega_i represent the resonance frequencies of the two oscillators and the \gamma_i their damping rates.

### Complex number

**complexreal partimaginary part**

Changing variables to the complex parameters, allows us to write these as first-order equations:

### Rotating wave approximation

**rotating-wave approximationrapidly rotating'' in the frame of the atom**

Finally, we make a rotating wave approximation, neglecting the fast counter-rotating terms proportional to, which average to zero over the timescales we are interested in (this approximation assumes that, which is reasonable for small frequency ranges around the resonances).

### Angular frequency

**angular rateangular speedangular frequencies**

:Without damping, driving or coupling, the solutions to these equations are, which represent a rotation in the complex \alpha plane with angular frequency \Delta.

### Steady state

**steady-stateequilibriumsteady**

The steady-state solution can be found by setting, which gives:

### Spectral density

**frequency spectrumpower spectrumspectrum**

Note that there is no antiresonance in the undriven oscillator's spectrum; although its amplitude has a minimum between the normal modes, there is no pronounced dip or negative phase shift.