“forced oscillations”的概念、定义、翻译、参考文献-科学参考

forced oscillations

Mathematics

Oscillations that occur when a body capable of oscillating is subject to an applied force which varies with time. If the applied force is itself oscillatory, a differential equation such as $m \ddot{x} + k x = F_{0} sin (Ω t + ε)$ may be obtained. The natural frequency of this system equals $\sqrt{k / m}$ , and if the forced frequency Ω‎ agrees with the natural frequency, then resonance will occur.
http://www.acoustics.salford.ac.uk/feschools/waves/shm3.htm Animations and videos of forced oscillation and resonance.

Electronics and Electrical Engineering

Oscillations produced in a circuit that is acted upon by an external driving force, such as oscillations in a resonant circuit coupled to a fixed-frequency oscillator. The resulting oscillations have two components: a transient component, whose frequency is determined by the natural frequency of the circuit and decays rapidly, and a steady component, whose frequency equals that of the external driving force.
If a circuit is acted upon by an external voltage
$V = V_{o} cos ω t$
applied at t = 0, then the steady-state solution is given by
$I = (\frac{V_{o}}{Z}) cos (ω t - ϕ)$
where Z is the impedance and is given by
$Z^{2} = R^{2} + {(ω L - \frac{1}{ω C})}^{2}$
and ϕ, the phase angle, is given by
$ϕ = {tan}^{- 1} [\frac{(ω L - \frac{1}{ω C})}{R}]$
The phase differs from that of the applied voltage except when
$ω L - \frac{1}{ω C} = 0,$
i.e when
$ω = ω_{0} = \frac{1}{\sqrt{(L C)}}$
where ω₀ is the natural frequency of the circuit. This is the resonance condition and the current is then a maximum. See also resonant frequency; free oscillations.

单词	forced oscillations
释义	forced oscillations Mathematics Oscillations that occur when a body capable of oscillating is subject to an applied force which varies with time. If the applied force is itself oscillatory, a differential equation such as $m \ddot{x} + k x = F_{0} sin (Ω t + ε)$ may be obtained. The natural frequency of this system equals $\sqrt{k / m}$ , and if the forced frequency Ω‎ agrees with the natural frequency, then resonance will occur. http://www.acoustics.salford.ac.uk/feschools/waves/shm3.htm Animations and videos of forced oscillation and resonance. Electronics and Electrical Engineering Oscillations produced in a circuit that is acted upon by an external driving force, such as oscillations in a resonant circuit coupled to a fixed-frequency oscillator. The resulting oscillations have two components: a transient component, whose frequency is determined by the natural frequency of the circuit and decays rapidly, and a steady component, whose frequency equals that of the external driving force. If a circuit is acted upon by an external voltage $V = V_{o} cos ω t$ applied at t = 0, then the steady-state solution is given by $I = (\frac{V_{o}}{Z}) cos (ω t - ϕ)$ where Z is the impedance and is given by $Z^{2} = R^{2} + {(ω L - \frac{1}{ω C})}^{2}$ and ϕ, the phase angle, is given by $ϕ = {tan}^{- 1} [\frac{(ω L - \frac{1}{ω C})}{R}]$ The phase differs from that of the applied voltage except when $ω L - \frac{1}{ω C} = 0,$ i.e when $ω = ω_{0} = \frac{1}{\sqrt{(L C)}}$ where ω₀ is the natural frequency of the circuit. This is the resonance condition and the current is then a maximum. See also resonant frequency; free oscillations.
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