What Is the Correct Inverse Laplace Transform of 1/s(s²+w²)?

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Discussion Overview

The discussion centers around finding the inverse Laplace transform of the function 1/s(s²+w²). Participants explore the use of partial fraction decomposition and share their calculations and results, seeking clarification on discrepancies in their findings.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using partial fraction decomposition to express 1/s(s²+w²) as A/s + Bs + C/(s²+w²) and calculates A=1/w², B=-1, and C=0.
  • Another participant agrees with the values for A and C but challenges the value of B, suggesting a different approach to find it.
  • Participants discuss the method of comparing coefficients to derive the values of A, B, and C, leading to a consensus that A + B = 0 and Aw² = 1.
  • One participant expresses uncertainty about the correctness of their inverse Laplace transform result, which they state as 1/w² - cos(wt).
  • A later reply suggests that the inverse Laplace transform could be expressed as 1/w²[1 - cos(wt)], indicating a potential refinement of earlier calculations.

Areas of Agreement / Disagreement

Participants generally agree on the values of A and C, but there is disagreement regarding the value of B and the correctness of the inverse Laplace transform results. The discussion remains unresolved as participants continue to explore different approaches and calculations.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in finding the inverse Laplace transform, and there are dependencies on the definitions and assumptions made during the decomposition process.

engnrshyckh
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TL;DR
I want to find inverse laplace of function 1/s(s^2+w^2)
I used partial fraction method first as:
1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
I found A=1/w^2
B=-1
C=0
1/s(s^2+w^2)=1/sw^2- s/s^2 +w^2
Taking invers laplace i get
1/w2 - coswt
But the ans is not correct kindly help.
 
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engnrshyckh said:
Summary:: I want to find inverse laplace of function 1/s(s^2+w^2)

I used partial fraction method first as:
1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
I found A=1/w^2
B=-1
C=0
I agree with your answers for A and C, but I get something different for B.
engnrshyckh said:
1/s(s^2+w^2)=1/sw^2- s/s^2 +w^2
Taking invers laplace i get
1/w2 - coswt
But the ans is not correct kindly help.
 
Mark44 said:
I agree with your answers for A and C, but I get something different for B.
Tell me?
 
engnrshyckh said:
Tell me?
Comparing the Coefficient of s^2 i get (1+B)/w^2 =0 which give me B=-1
 
engnrshyckh said:
Summary:: I want to find inverse laplace of function 1/s(s^2+w^2)

1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
Multiply both sides by ##s(s^2 + w^2)##. What do you get in the next step?
 
Mark44 said:
Multiply both sides by ##s(s^2 + w^2)##. What do you get in the next step?
1=A(s^2+w^2)+BS^2+Cs
 
engnrshyckh said:
1=A(s^2+w^2)+BS^2+Cs
For finding B
As^2+Bs^2=0
 
engnrshyckh said:
For finding B
As^2+Bs^2=0
Right, so A + B = 0, and also Aw^2 = 1, so what do you now get for B?
 
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Mark44 said:
Right, so A + B = 0, and also Aw^2 = 1, so what do you now get for B?
Thanks - 1/w2
 
  • #10
engnrshyckh said:
Thanks - 1/w2

1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
=1/w^2(1/s-s/s^2+w^2) taking inverse laplace ibget
=1/w^2[1-coswt)
 

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