Help with Inverse Laplace Transform

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Discussion Overview

The discussion revolves around finding the Inverse Laplace Transform of a given transfer function, specifically H(s) = 1 / (s^2 + 20s + 5K), where K is an unknown constant. The scope includes mathematical reasoning and technical explanation related to Laplace transforms.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance with the Inverse Laplace Transform due to the loss of data sheets.
  • Another participant suggests completing the square as a potential method for solving the problem.
  • A participant proposes a form for the inverse transform as h(t) = e^(-10t)*sin(sqrt(5K-100)t), indicating a dependence on the constant K.
  • A later reply corrects the previous expression by adding the missing 't' in the sine function, presenting h(t) = e^(-10t)*sin(sqrt(5K-100)t).

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints on how to approach the problem, with no consensus reached on the final form of the inverse transform or the value of K.

Contextual Notes

The proposed solutions depend on the value of K, which remains undetermined, and the mathematical steps for completing the square have not been elaborated upon.

nick_d_g
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Hello,
I know normally giving solutions is frowned upon, but I have lost my colleagues data sheets and desperately need this transform to continue my work.
I am looking for the Inverse Laplace Transform of the Transfer Function:

H(s) = 1 / (s^2 + 20s + 5K)

where K is an as yet unknown constant, to be determined using this result.

Any help with this would be muchly appreciated.
Many Thanks
Nickxx
 
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Try completing the square.
 
h(t)=e^(-10t)*sin(sqrt(5k-100))
 
I forgot the t in the sine function and it wouldn't let me edit my post:
h(t)=e^(-10t)*sin(sqrt(5k-100)t)
 

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