 ## Welcome!

The ABRAVIBE blog is where you find all the resources for learning more about vibrations. Browse and download examples for the free MATLAB/Octave ABRAVIBE toolbox. Or browse the many theory examples, videos, and resources for the book "Noise and Vibration Analysis: Signal Analysis and Experimental Procedures," by Anders Brandt!

## Theory problem: forced response of SDOF system to half-sine excitation by Laplace transform

Theory Examples Posted on Mar 03, 2013 15:40

This is an example of using the Laplace transform to solve the forced response of a mechanical system. In this example the system is excited by a half-sine pulse, which is common in, for example, vibration testing. The supplied zip file contains a pdf file with the problem definition, and a separate zip file with a suggested solution. Like the harmonic SDOF forced response example, the present example is also an example I let all my mechanical vibration students solve. You can download the example either by signing in and browse the resources, or by clicking here.

## Theory problem: forced response of SDOF system to harmonic excitation by Laplace transform

Theory Examples Posted on Feb 26, 2013 20:21

This an example of using the Laplace
transform to solve the forced response of a mechanical system. It is
also an illustration of the so-called beating phenomenon that can occur
if a dynamic system is suddenly exposed to a harmonic excitation close
to a natural frequency of the system. As illustrated by this example,
the beating phenomenon occurs is more pronounced when damping is low.
The supplied zip file contains a pdf file with the problem definition,
and a separate zip file with a suggested solution. I run this example with all my mechanical vibration students, since it is a good example of how to use the Laplace transform to solve forced response. It is, of course, also an important demonstration example to run for different system damping and excitation frequencies, to learn the concept of beating and to understand the harmonic response of a SDOF system. Download the file by signing in and selecting it on the download page. Or, if you are signed-in already, click on the link in the text above!