Let ω0≠ω, need solve y′′+ω20y=sin(ωt) by Laplace transform using the initial conditions y(0)=0, and y′(0)=0.

Parker Pitts

Parker Pitts

Answered question

2022-09-29

Let ω 0 ω, need solve y + ω 0 2 y = sin ( ω t ) by Laplace transform using the initial conditions y(0)=0, and y′(0)=0.
I have gotten down as far as the partial fraction decomposition being this, ω ( s 2 + ω 0 2 ) ( s 2 + ω 2 ) but am confused as how to proceed from there.

Answer & Explanation

Frederick Espinoza

Frederick Espinoza

Beginner2022-09-30Added 7 answers

From
A ( s 2 + ω 2 ) + B ( s 2 + ω 0 2 ) = ( A + B ) s 2 + ( A ω 2 + B ω 0 2 ) = 1 ,
you get
A + B = 0 , A ω 2 + B ω 0 2 = 1 ,
where you can solve for A and B. Only s is considered as a variable here; ω and ω 0 are constants

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