How do you find the Laplace transform of a Dirac delta function?
The Laplace transform of the Dirac delta function is easily found by integration using the definition of the delta function: Lδ(t−c)=∫∞0e−stδ(t−c)dt=e−cs.
What is the Laplace of 5?
Thus, if we have a step input of size 5 at time t=0 then the Laplace transform is five times the transform of a unit step and so is 5/s. If we have an impulse of size 5 at time t=0 then its transform is 5.