Laplace transform is a mathematical tool that converts a function of a real variable to a function of a complex variable s (complex frequency). It is used for solving differential equations. Here is the Laplace transform table.
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Laplace transform table
S.No. | Function | Laplace transform |
1. | 1 |
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2. | eat |
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3. | e−at |
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4. | tn , where n= 1,2,3,…… |
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5. | tp , p > -1 |
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6. | tn eat, where n= 1,2,3,…… |
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7. |
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8. | tn-½ , where n= 1,2,3,…… |
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9. | sin(at) |
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10. | cos(at) |
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11. | t sin(at) |
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12. | t cos(at) |
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13. | sin(at) − at cos(at) |
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14. | sin(at) + at cos(at) |
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15. | cos(at) − at sin(at) |
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16. | cos(at) + at sin(at) |
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17. | sin(at + b) |
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18. | cos(at + b) |
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19. | sinh(at) |
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20. | cosh(at) |
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21. | eat sin(bt) |
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22. | eat cos(bt) |
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23. | eat sinh(bt) |
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24. | eat cosh(bt) |
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25. | t sinh(bt) |
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26. | t cosh(bt) |
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Laplace Transform Properties Table
Let F(s) be the laplace transform of f(t) i.e.
S.No. | Function | Laplace transform |
1. | f(at) |
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2. | f(t-a) |
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3. | eat f(t) |
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4. | tn f(t) |
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5. |
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6. |
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7. |
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8. |
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9. |
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10. |
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General functions Laplace transform Table
S.No. | Function | Laplace transform |
1. | δ(t) |
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2. | δ(t-a) |
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3. | u(t) |
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4. | u(t-a) |
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5. | r(t) |
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