# Relationship between damping and resonance frequency

### Damping , resonance and natural frequency? | Physics Forums

The amplitude of the motion of the weight is maximum when the drive frequency equals the natural frequency. This condition is called a resonance. A damped. Like asking what is the relationship between a banana, steak and chunk of gravel . They are all matter. Those three term are all parameters of. If an object is being forced to vibrate at its natural frequency, resonance will The phase relationship between the driving oscillation and the the oscillation of.

Furthermore, the structure is designed to resonate at a frequency that does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition, engineers designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.

Clocks keep time by mechanical resonance in a balance wheelpendulumor quartz crystal. The cadence of runners has been hypothesized to be energetically favorable due to resonance between the elastic energy stored in the lower limb and the mass of the runner.

This is the source of many percussive sounds we hear. Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonatorssuch as the strings and body of a violinthe length of tube in a fluteand the shape of, and tension on, a drum membrane. Like mechanical resonance, acoustic resonance can result in catastrophic failure of the object at resonance. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass, although this is difficult in practice.

Electrical resonance Animation illustrating electrical resonance in a tuned circuitconsisting of a capacitor C and an inductor L connected together. Charge flows back and forth between the capacitor plates through the inductor. Energy oscillates back and forth between the capacitor's electric field E and the inductor's magnetic field B. Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedance of the circuit is at a minimum in a series circuit or at maximum in a parallel circuit or when the transfer function is at a maximum.

## Forced Vibrations & Resonance

Resonance in circuits are used for both transmitting and receiving wireless communications such as television, cell phones and radio. Optical cavity An optical cavityalso called an optical resonator, is an arrangement of mirrors that forms a standing wave cavity resonator for light waves.

Optical cavities are a major component of laserssurrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times producing standing waves for certain resonant frequencies. The standing wave patterns produced are called "modes".

Longitudinal modes differ only in frequency while transverse modes differ for different frequencies and have different intensity patterns across the cross-section of the beam.

Ring resonators and whispering galleries are examples of optical resonators that do not form standing waves. Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them; flat mirrors are not often used because of the difficulty of aligning them precisely.

### Resonance - Wikipedia

The geometry resonator type must be chosen so the beam remains stable, i. Resonator types are also designed to meet other criteria such as minimum beam waist or having no focal point and therefore intense light at that point inside the cavity. Optical cavities are designed to have a very large Q factor. Additional optical resonances are guided-mode resonances and surface plasmon resonancewhich result in anomalous reflection and high evanescent fields at resonance.

## More on damping

In this case, the resonant modes are guided modes of a waveguide or surface plasmon modes of a dielectric-metallic interface. These modes are usually excited by a subwavelength grating. Orbital resonance In celestial mechanicsan orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers.

Orbital resonances greatly enhance the mutual gravitational influence of the bodies. They produce a hump with an exponential tail like when you jump on a car bumper.

This motion or electrical response would be the "natural behavior" of the system under those conditions. No frequencies are to be seen unless you want to call the exponential exponents "natural frequencies". You only get what you think of as oscillations with a frequency damped sin waves in the underdamped case. In this case the solutions do result in a "natural frequency".

**Forced Damped Vibrations**

And that "natural frequency" is the frequency of the oscillatory motion of the solutions. It is NOT the frequency of the undamped system! The solutions for such a system do reduce to the sin wave of the undamped case when damping is removed, but natural frequency of motion is given by a formula where the amount of damping tends to reduce the oscillating frequency from that found with an undamped system.

And the rate at which the 'natural frequency" dies out in an exponential decay also depends upon the amount of damping present. The frequency of the undamped case is called the "undamped frequency" Duh! Or to be strictly mathematically correct it is termed the "undamped imaginary frequency". The reason being that in advanced math "generalized frequencies" are considered where even non-oscillatory exponents are considered to be "frequencies".

So to answer your question. IF you have the oscillatory under-damped case, you will have a "natural frequency" which represents the natural frequency of the freely vibrating undriven oscillator in response to some initial conditions.