resonance

Examples of resonance in the following topics:

• Resonance in RLC Circuits

  • Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others.
  • $\nu_0$ is the resonant frequency of an RLC series circuit.
  • Resonance in AC circuits is analogous to mechanical resonance, where resonance is defined as a forced oscillation (in this case, forced by the voltage source) at the natural frequency of the system.
  • A variable capacitor is often used to adjust the resonance frequency to receive a desired frequency and to reject others. is a graph of current as a function of frequency, illustrating a resonant peak in Irms at $\nu_0 = f_0$.
  • Both have a resonance at f0, but that for the higher resistance is lower and broader.

• NMR and MRIs

  • Magnetic resonance imaging is a medical imaging technique used in radiology to visualize internal structures of the body in detail.
  • Magnetic resonance imaging (MRI), also called nuclear magnetic resonance imaging (NMRI) or magnetic resonance tomography (MRT), is a medical imaging technique used in radiology to visualize internal structures of the body in detail.
  • MRI utilized the property of nuclear magnetic resonance (NMR) to image the nuclei of atoms inside the body.
  • This electromagnetic field has just the right frequency (known as the resonance frequency) to become absorbed and then reverse the rotation of the hydrogen protons in the magnetic field.

• Forced Vibrations and Resonance

  • The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance.
  • The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance.
  • It is interesting that the widths of the resonance curves shown in depend on damping: the less the damping, the narrower the resonance.
  • In all of these cases, the efficiency of energy transfer from the driving force into the oscillator is best at resonance.
  • Heavy cross winds drove the bridge into oscillations at its resonant frequency.

• Standing Waves in Air Columns

  • We use specific terms for the resonances in any system.
  • The lowest resonant frequency is called the fundamental, while all higher resonant frequencies are called overtones.
  • Now let us look for a pattern in the resonant frequencies for a simple tube that is closed at one end.
  • The resonant frequencies of a tube closed at one end are:
  • Simple resonant cavities can be made to resonate with the sound of the vowels, for example.

• Standing Waves and Resonance

  • A closer look at earthquakes provides evidence for conditions appropriate for resonance: standing waves, and constructive and destructive interference.
  • A building may be vibrated for several seconds with a driving frequency matching that of the natural frequency of the vibration of the building—producing a resonance resulting in one building collapsing while neighboring buildings do not.

• Driven Oscillations and Resonance

  • For a particular driving frequency called the resonance, or resonant frequency $\!
  • This resonance effect only occurs when $\zeta < 1 / \sqrt{2}$, i.e. for significantly underdamped systems.
  • For strongly underdamped systems the value of the amplitude can become quite large near the resonance frequency (see ).

• Power

  • For example, at the resonant frequency $(\nu_0 = \frac{1}{2\pi \sqrt{LC}})$ or in a purely resistive circuit, Z=R, so that cosϕ=1.
  • At other frequencies, average power is less than at resonance, because voltage and current are out of phase and Irms is lower.
  • At the resonant frequency, cosϕ=1.
  • The amplitude of the wheels' motion is a maximum if the bumps in the road are hit at the resonant frequency.
  • The mass and spring determine the resonant frequency.

• Forced motion with damping

  • Figure 1.9: Resonance ultrasonic spectroscopy setup.
  • As the frequency is varied we see the characteristic resonance (cf Figure 1.8).
  • Figure 1.8: Here is a resonance spectrum for a piece of aluminum about the size shown in Figure 1.9.
  • At a resonant frequency, there is a big jump in the amplitude.
  • Square of the amplitude factor for forced, damped motion near a resonance $\omega_0$.

• Examples and Applications

  • To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency,
  • As electrons sweep past these openings, they induce a resonant, high-frequency radio field in the cavity, which in turn causes the electrons to bunch into groups.
  • The sizes of the cavities determine the resonant frequency, and thereby the frequency of emitted microwaves.
  • A cross-sectional diagram of a resonant cavity magnetron.

• Pictures of Modes

  • The plate is attached via a screw through a hole in the middle to a resonator.