Laplace Transform Examples Part 1
Let us solve the Laplace Transform Examples for clearing our concept,
1) Where, F(s) is the Laplace form of a time domain function f(t). Find the expiration of f(t). Answer Now, Inverse Laplace Transformation of F(s), is
2) Find Inverse Laplace Transformation function of Answer
3) Solve the differential equation Answer As we know that, Laplace transformation of4) Solve the differential equation, Answer
As we know that,
5) For circuit below, calculate the initial charging current of capacitor using Laplace Transform technique.
The above figure can be redrawn in Laplace form, Now, initial charging current, 6) Solve the electric circuit by using Laplace transformation for final steady-state current Answer
The above circuit can be analyzed by using Kirchhoff Voltage Law and then we get Final value of steady-state current is 7) A system is represented by the relation Where, R(s) is the Laplace form of unit step function. Find the value of x(t) at t → ∞.
As R(s) is the Laplace form of unit step function, it can be written as
Answer 8) Find f(t), f'(t) and f"(t) for a time domain function f(t). The Laplace Transformation form of the function is given as By applying initial value theorem, we get, Applying Initial Value Theorem, we get, More Examples on Laplace Transform