Module 4 : Laplace and Z Transform
Problem 7 : Inverse Laplace and Z Transform of Rational Functions
 
Solution 7:  

            The given model is a LTI system.

When the given system is fed with the input , the output produced is . Hence, the system function H(s), is the ration of the Laplace transform of the output divided by the Laplace transform of the input.

÷ 

Now, for the given input , the observed output

Let the Laplace transforms of the input and the output be and .                                                                                  

We know that,

  {Method of partial fractions}

Therefore, the true pressure input to the gauge is                                                       

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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