Laplace Transform

The Laplace Transform is a method to solve some differential equations. Given that is a piecewise continuous function for . The Laplace transform for is:

Where is a complex-number, when talking about mechanical systems it looks like where is the frequency.

Taking the Laplace of a function turns differentiation and integration operations into multiplication and division and therefor greatly simplifying operations. The following in addition to a Laplace Transform Table can be used to transform a function to and from its Laplace.

See W4L1 - Intro to Laplace Transforms and W4L2 - Calculating the Laplace Transform for examples and more information.

Undoing a Laplace Transform is called finding the Inverse Laplace Transform, . See W4L4 - Basic Inverse Laplace Transforms, W4L5 - Inverse Laplace Transform, W4L6 - Laplace Transform Basic Properties, and Chapter 7.2 - Inverse Transforms and Transforms of Derivatives for more information and examples.