# Relationship between damping and resonance definition

### Resonance - Wikipedia

The definition of these items are: Natural Frequency: All physical structures A mass-spring-damper system is a simplified representation that is useful for yields some interesting phase relationships as shown in Figure 4. It is interesting that the widths of the resonance curves shown in [link] depend on damping: the less the damping, the narrower the resonance. The message is. When a forced oscillation is damped, it is true that the frequency at which resonance It depends on your definition of "natural frequency". The other attached image is of amplification factor vs. resonant frequency ratio for a.

Amplitude Response A force f can be applied to the object and the frequency response in displacement x or acceleration acan be plotted as shown in Figure 3. Left - Displacement response compliance graph of mass-spring-damper system due to force as function of frequency. Right — Acceleration response accelerance graph of same. Other amplitude response observations include: Below the resonant frequency, the response of the system can be said to be stiffness dominated.

Above the resonant frequency, the response of the system can be said to be dominated by the mass. Knowing about these stiffness or mass regions can be useful in reducing vibration levels away from the resonance. Phase Response Applying the force through a moving base, and observing the mass response, yields some interesting phase relationships as shown in Figure 4.

SDOF system response below, at, and above natural frequency of system. The following can be observed: Below the natural frequency, the base and mass move together in phase.

• AQA A-Level Physics/Forced Vibrations, Damping and Resonance
• More on damping
• Forced Vibrations & Resonance

Above the resonant frequency, the base and mass move out of phase. Real world objects, from cars to airplanes to washing machines, can be thought of a collection of mass, stiffness, and damping elements. They have many natural frequencies. Finite element models, used in calculating natural frequencies virtually, use this approach. The equation is a quadratic and you'll find that these solutions have three cases. Two of these solutions produce solutions roots of the "impedance" that are not "oscillations" in the normal sense at all.

That would be the over-damped and critically damped cases. 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".

And that "natural frequency" is the frequency of the oscillatory motion of the solutions.

### Simple Harmonic Motion SHM | A Level Physics Revision | University of Salford

These oscillations were captured on video, and lasted for seconds. Mechanical resonanceAcoustic resonanceand String resonance School resonating mass experiment Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, trains, and aircraft.

When designing objects, engineers must ensure the mechanical resonance frequencies of the component parts do not match driving vibrational frequencies of motors or other oscillating parts, a phenomenon known as resonance disaster. Avoiding resonance disasters is a major concern in every building, tower, and bridge construction project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy.

The Taipei building relies on a tonne pendulum short-ton —a tuned mass damper —to cancel resonance. 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.

## Damping , resonance and natural frequency?

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.