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Laplace Transform Examples Part 1

on 24/2/2012 & Updated on Saturday 14th of July 2018 at 07:19:03 PM

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

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Laplace Transform Examples Part 1

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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