Laplace transform of x

1. What is the Laplace transform of X?
2. What is the Laplace transform of 1?
3. What is the Laplace transform of Y?
4. What is Laplace transform of 0?

What is the Laplace transform of X?

It is a linear transformation which takes x to a new, in general, complex variable s. It is used to convert differential equations into purely algebraic equations.

What is the Laplace transform of 1?

The Laplace transforms of particular forms of such signals are: A unit step input which starts at a time t=0 and rises to the constant value 1 has a Laplace transform of 1/s. A unit impulse input which starts at a time t=0 and rises to the value 1 has a Laplace transform of 1.

What is the Laplace transform of Y?

Y (s) = F(s) + αs + β + aα s2 + as + b . Implicit in these derivations is the assumption that the Laplace transform of y and its derivatives exist. Assuming that this is the case, the importance of these results is that it gives us the Laplace transform of the solution of an initial-value problem directly.

What is Laplace transform of 0?

The function F(s) is called the Laplace transform of the function f(t). Note that F(0) is simply the total area under the curve f(t) for t = 0 to infinity, whereas F(s) for s greater than 0 is a "weighted" integral of f(t), since the multiplier e^–st is a decaying exponential function equal to 1 at t = 0.