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

[engnrshyckh]

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.

 

[Mark44]

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.

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.

 

[engnrshyckh]

I agree with your answers for A and C, but I get something different for B.

Tell me?

 

[engnrshyckh]

Tell me?

Comparing the Coefficient of s^2 i get (1+B)/w^2 =0 which give me B=-1

 

[Mark44]

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?

 

[engnrshyckh]

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]

1=A(s^2+w^2)+BS^2+Cs

For finding B
As^2+Bs^2=0

 

[Mark44]

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?

 

[engnrshyckh]

Right, so A + B = 0, and also Aw^2 = 1, so what do you now get for B?

Thanks - 1/w2

 

[engnrshyckh]

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)