the laplace transforms
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/1.jpg)
PART 1
THE LAPLACE TRANSFORMS
![Page 2: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/2.jpg)
6.2. Defination of Laplace Transform
![Page 3: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/3.jpg)
6.2. Defination of Laplace Transform
a)
![Page 4: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/4.jpg)
b)
c)
![Page 5: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/5.jpg)
Example 6.2.
Solution:
![Page 6: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/6.jpg)
Hence;
6.3. Properties of Laplace Transform1. Linearity
![Page 7: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/7.jpg)
6.3. Properties of Laplace Transform2. Scalling
![Page 8: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/8.jpg)
3. Time Shift
![Page 9: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/9.jpg)
6.3. Properties of Laplace Transform
![Page 10: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/10.jpg)
?
6.3. Properties of Laplace Transform
![Page 11: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/11.jpg)
6.3. Properties of Laplace Transform4. Frequency Shift
![Page 12: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/12.jpg)
6.3. Properties of Laplace Transform5. Time Differantiation
![Page 13: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/13.jpg)
6.3. Proporties of Laplace Transform
![Page 14: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/14.jpg)
6.3. Properties of Laplace Transform
![Page 15: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/15.jpg)
6.3. Properties of Laplace Transform6. Time Integration
![Page 16: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/16.jpg)
6.3. Properties of Laplace Transform
![Page 17: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/17.jpg)
6. Frequency Differantiation
6.3. Properties of Laplace Transform
![Page 18: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/18.jpg)
7. Time Periodicity
![Page 19: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/19.jpg)
Taking Laplace transform of each term;
![Page 20: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/20.jpg)
8. Initial and Final Values
For initial values;
For an example;
Then;
![Page 21: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/21.jpg)
For Final Value;
For Example;
![Page 22: THE LAPLACE TRANSFORMS](https://reader033.vdocuments.site/reader033/viewer/2022061415/5681610a550346895dd05671/html5/thumbnails/22.jpg)
As another example;
This is incorrect !!!!