Download Laplace transforms and Physics equations. http://people.seas

Laplace transforms and Physics equations.
http://people.seas.harvard.edu/~jones/es154/lectures/lecture_0/Laplace/laplace.html
RLC Circuits
An Example of the Application of Laplace Transforms
Kirchoff's voltage law
Kirchoff's voltage law transformed
where
Example 1 - A series RLC circuit excited by a unit impulse function - that is to
say
(The unit impulse always gives the "natural response" of any circuit.
Natural as compared to "forced" response.)
This is to be compared to the transform pair
See the table of Laplace transform pairs
Therefore, if
where
Good discussion, examples from MSU Carefully study the treatment of the oscillator.
http://physnet2.pa.msu.edu/home/modules/pdf_modules/m47.pdf
Explanation, examples:
http://claymore.engineer.gvsu.edu/~jackh/books/model/chapters/laplace.pdf
Damped spring and mass oscillator example http://www.vibrationdata.com/tutorials2/free.pdf
Table of Laplace trasforms http://www.vibrationdata.com/math/Laplace_Transforms.pdf