 Welcome back MechanicalEI. Did you know that HeavisideUnit function represents switches or similar functions whose values suddenly change with time? This makes us wonder, what is HeavisideUnit step function? Before we jump in, check out the previous part of this series to learn about what linearity property is. First, let's see what the first shifting property of Laplace Transform is. Consider Laplace transformation of f of t is f of s and s is greater than a. Then the first shifting property states that the Laplace Transform of e power at f of t is equal to f of s minus a. In other words, the substitution of s minus a for s in the transform corresponds to the multiplication of the original function by e power at. A HeavisideUnit function is defined as a function say u of t equals zero for t less than c and equals q if t is greater than c. It can be visualized as a mathematical switch that turns on when the value in the x-axis crosses c. The graphs can be of any type and not only constants. To deal with the Laplace Transform of such functions, second shifting property is employed. It states that if Laplace Transform of f of t is equal to f of s and g is a Heaviside function with g of t equals f of t minus a for t greater than a and g of t equals zero for t less than a, then Laplace Transform of g of t is e power minus a s into f of s. So whatever the value is subtracted from t in the on switch part of g of t, it is simply multiplied by minus t in the power of e. Hence, we first saw what first shifting property of Laplace Transforms are and then went on to see what Heaviside unit function is and how second shifting function is related to it.