 Welcome back MechanicalEI, did you know the graphs of voltage and current across a resistor exhibit linearity property and even mass and weight exhibit linearity property? This makes us wonder, what is linearity property? Before we jump in, check out the previous part of the series to learn about what Laplace transforms are. First, let's look at a few common Laplace transforms of standard functions. The Laplace transform of 1 is 1 upon s. For t to the power n is n factorial upon s power n plus 1, Laplace transform of e power at is 1 upon s minus a. For trigonometric functions like sin at and cos at, it is a upon s squared plus a squared and s upon s squared plus a squared respectively. For hyperbolic trigonometric functions like sin h at and cos h at, the respective Laplace transforms are a upon s squared minus a squared and s upon s squared minus a squared. Having noun these small but significant quantity of identities, we'll look at the linearity property of Laplace transforms. The linearity property states that if a and b are constants, well f of t and g of t are functions of t, whose Laplace transform exists, then Laplace transform of the sum given by a of f of t and b of g of t is equal to a multiplied by Laplace transform of f of t plus b multiplied by Laplace transform of g of t. This property can be easily extended to more than two functions. With the linearity property, Laplace transform can also be called the linear operator. Hence, we first saw what Laplace transforms of standard functions are and then went on to see what linearity property of Laplace transform is. 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 helped the channel grow. So, here are the top Mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what haveside unit function is.