THE LAPLACE TRANSFORMS

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THE LAPLACE TRANSFORMS. PART 1. 6.2. Defination of Laplace Transform. 6.2. Defination of Laplace Transform. a). b ). c ). Example 6.2. Solution:. 6.3. Prop e rties of Laplace Transform. 1. Linearity. Hence ;. 6.3. Prop e rties of Laplace Transform. 2. Scalling. 3. Time Shift. - PowerPoint PPT Presentation

Text of THE LAPLACE TRANSFORMS

THE LAPLACE TRANSFORMS

PART 1THE LAPLACE TRANSFORMS6.2. Defination of Laplace Transform

6.2. Defination of Laplace Transform

a)b)

c)

Example 6.2.Solution:

Hence;

6.3. Properties of Laplace Transform1. Linearity

6.3. Properties of Laplace Transform2. Scalling

3. Time Shift

6.3. Properties of Laplace Transform

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6.3. Properties of Laplace Transform

6.3. Properties of Laplace Transform4. Frequency Shift

6.3. Properties of Laplace Transform5. Time Differantiation

6.3. Proporties of Laplace Transform

6.3. Properties of Laplace Transform

6.3. Properties of Laplace Transform6. Time Integration6.3. Properties of Laplace Transform

6. Frequency Differantiation

6.3. Properties of Laplace Transform

7. Time Periodicity

Taking Laplace transform of each term;

8. Initial and Final Values

For initial values;For an example;

Then;

For Final Value;For Example;

As another example;

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