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Impulse Response

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...

Series RLC Circuit with Source

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Consider the operation of an automobile ignition system, a crucial component responsible for generating a spark by producing high voltage from the battery. This system can be described as a simple series RLC circuit, allowing for an in-depth analysis of its complete response.
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Parallel RLC Circuits

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Street lamps equipped with RLC surge protectors are an excellent example of applying circuit analysis in practical scenarios. These surge protectors safeguard the lamp's components against sudden voltage spikes.
A simplified parallel RLC circuit model with a DC input source generating a step response is employed in this context. When the switch is turned on, Kirchhoff's current law is applied, leading to a second-order differential equation.

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An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
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Series RLC Circuit without Source

Series RLC Circuit without Source

Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...

Types of Responses of Series RLC Circuits

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A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.

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Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

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Causal impulse response for circular sources in viscous media.

James F Kelly¹, Robert J McGough

¹Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA. kellyja8@msu.edu

The Journal of the Acoustical Society of America

|April 10, 2008

Summary

This study introduces a new time-domain method for calculating transient velocity potential fields in viscous media, improving accuracy for Stokes wave phenomena.

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Area of Science:

Fluid dynamics
Acoustics
Wave propagation

Background:

Transient velocity potential fields are crucial in understanding wave phenomena in viscous media.
Previous methods often relied on frequency-domain analysis, requiring complex inverse transforms.
Accurate modeling of viscous effects, including attenuation, is essential for realistic simulations.

Purpose of the Study:

To derive and verify a causal impulse response for the Stokes wave equation.
To calculate the lossy impulse response for baffled circular pistons in viscous media.
To compare time-domain calculations using the lossy impulse response with lossless approximations.

Main Methods:

Derivation of the causal impulse response for the Stokes wave equation.
Numerical verification using the material impulse response function approach.
Calculation of the causal, lossy impulse response in near and far fields using the fast near field method.
Direct time-domain computation of transient velocity potential fields.

Main Results:

The causal, lossy impulse response was successfully calculated and verified.
Transient velocity potential fields were computed and compared between lossy and lossless models.
Numerical errors were analyzed, showing larger errors near the piston face and for longer relaxation times.
The new method avoids inverse Fourier transforms required by frequency-domain approaches.

Conclusions:

The derived causal impulse response enables direct time-domain calculations of viscous wave phenomena.
This approach accurately accounts for both diffraction and frequency-dependent attenuation.
The method offers an efficient alternative to frequency-domain techniques for transient wave field analysis.