 Welcome back MechanicalEI! Did you know that Thomas John E. Anson Brownwich, born in 1875, first used inverse Laplace transforms to justify operator calculus? This makes us wonder, what are inverse Laplace transformations? Before we jump in, check out the previous part of the series to learn about what direct delta function is. Now, if the Laplace transform of a function g of t is the piecewise continuous and exponentially restricted real function capital G of s then inverse Laplace transform of capital G of s denoted as L to the power minus 1 capital G of s equals G of t. There are two common properties that are essential to inverse Laplace transforms. First is the linearity property which states that Laplace inverse of A into capital G1 of s plus B into capital G2 of s equals A into G1 of t plus B into G2 of t. The second property is shifting property which states that if Laplace inverse of capital G of s equals G of t then Laplace inverse of capital G of s minus A equals e power A t into G of t. Let's look at some common inverse Laplace forms and their transforms. The Laplace inverse of 1 upon s is 1. Laplace inverse of 1 upon s minus A is e power A t. For n factorial upon s power n plus 1 it is t to the power n where n is any positive integer greater than 0. Laplace inverse for a upon s squared plus a squared is sine A t and for s upon s squared plus a squared is cos A t. Finally, the inverse Laplace transform of s upon s squared minus a squared is cos h A t and a upon s squared minus a squared is sine h A t. Hence, we first saw what inverse Laplace transforms and their linearity property are and then went on to see the inverse Laplace transforms of a few common functions. So like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You help the channel grow. So, here are the top mechanical EIs of our last videos.