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foo9008
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Homework Statement
(2s^2) +10s / (s^2 -2s +5 )(s+1) , I have checked the partial fraction , it's correct , but according to the ans it's (e^t)[(3cos2t + 2.5sin2t)] - (e^-t), but my ans is (e^t)[(3cos2t + 4sin2t)] - (e^-t)
foo9008 said:Homework Statement
(2s^2) +10s / (s^2 -2s +5 )(s+1) , I have checked the partial fraction , it's correct , but according to the ans it's (e^t)[(3cos2t + 2.5sin2t)] - (e^-t), but my ans is (e^t)[(3cos2t + 4sin2t)] - (e^-t)Homework Equations
The Attempt at a Solution
Sorry, I mean the second one. You mean my answer is correct??Ray Vickson said:You typed
[tex] 2s^2 +\frac{10s}{(s^2 -2s +5 )(s+1)} [/tex]
If you mean
[tex] \frac{2s^2 + 10s}{(s^2-2s+5)(s+1)},[/tex]
you must either use LaTeX (as I did just now) or else use parentheses, like this:
(2s^2+ 10s)/[(s^2-2s+5)(s+1)]
Anyway, that form gives an inverse Laplace that agrees with your answer.
foo9008 said:Sorry, I mean the second one. You mean my answer is correct??
The Laplace transform of (2s^2 +10s) / ((s^2 -2s +5)(s+1)) is 2/s + 2/s^2 + 2/s^3 + 6/s^4.
The Laplace transform is a powerful mathematical tool used to solve differential equations and analyze systems in engineering, physics, and other fields. It allows us to transform a function from the time domain to the frequency domain, making it easier to solve complex problems.
1. Use partial fraction decomposition to break the rational function into simpler fractions.2. Apply the Laplace transform to each term separately.3. Use the properties of the Laplace transform to simplify the resulting expressions.4. Combine the terms back together to get the final answer.
The Laplace transform can only be applied to functions that are defined for all non-negative values of t. It cannot be used if the function has a discontinuity or an infinite discontinuity.
Yes, the inverse Laplace transform can be used to find the original function from its Laplace transform. However, this process can be complex and may require the use of tables or software. In this case, the inverse Laplace transform of 2/s + 2/s^2 + 2/s^3 + 6/s^4 would be the original function (2s^2 +10s) / ((s^2 -2s +5)(s+1)).