Electric Circuits and Networks

15.3 LAPLACE TRANSFORMS OF SOME COMMON RIGHT-SIDED FUNCTIONS

Integral of sum of two functions is the sum of integral of each function. Thus, Laplace transformation is a linear operation. If v₁(t) and v₂(t) are two right-sided functions and a₁ and a₂ are two real numbers, then, a₁v₁(t) + a₂v₂(t) ⇔ a₁ V₁(s) + a₂ V₂(s) is a Laplace transform pair. This is called Property of Linearity of Laplace transforms. Now, we work out the Laplace transforms for many commonly used right-sided functions using the defining integral and property of linearity.

 

Linearity property of Laplace transforms.

Let v(t) = e^s_otu(t) be a right-sided complex exponential function with a complex frequency of s_o. Then,

 

 

Therefore, e^s_otu(t) ⇔ 1/ (s – s_o) is a Laplace ...