Problems part 4 : Laplace Transform                                                                 

 

 

 

Example 1:  Find the Laplace transform of f(t)=a  

 

 

 

Example 2:

Consider the function of s :

 

  find the inverse Laplace

 

Answer

 

Applying the transform of sin , cos  we have :

 

 

 

Example 3

Consider the circuit when the switch is closed at t = 0 with V_C(0) = 1.0 V. Solve for the current i(t) in the circuit.

 

Answer

Multiplying throughout by  :

Taking Laplace transform:

Now in this example, we have the following initial conditions       .    So

That is:               

 

          Therefore:

 

 

 

NOTE:         

 

Collecting terms and subtracting from both sides:

So                 

 

 

 

Example 4 :

Find the inverse Laplace of  :  

 

 

Answer:

 

   We see that the numerator is of lower degree than denominator.

 

We can factorize the denominator   then    =

 

Working with partial fractions we have  :

 

  then A=3 and B=2.

 

 thus  applying properties

 

 

 

 

 

 

Go home

Go to first part : Principles of Signal and Systems Modeling Concepts

Go to second part : System Modeling and Analysis in the time domain

Go to third part : The Fourier series

Go to fourth part : Laplace Transform