# Laplace Transform Examples Part 1

Published on 24/2/2012 and last updated on Saturday 14th of July 2018 at 07:19:03 PMLet 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

Now, Hence,

3) Solve the differential equation Answer As we know that, Laplace transformation of

4) Solve the differential equation, Answer As we know that,

5) For circuit below, calculate the initial charging current of capacitor using Laplace Transform technique.

Answer 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

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