How to find the inverse laplace transform of this function: Y(s)=1/(tau s+1) xx (omega)/(s^2+omega^2) for omega, tau constant

KesseTher12

KesseTher12

Answered question

2022-10-05

How to find the inverse laplace transform of this function:
Y ( s ) = 1 τ s + 1 × ω s 2 + ω 2
for ω, τ constant

Answer & Explanation

Caiden Brewer

Caiden Brewer

Beginner2022-10-06Added 5 answers

you can apply convolution theorem
and seperate laplace transform of them are
1 τ s + 1 × ω s 2 + ω 2
laplace for 1st is
g ( t ) = 1 τ exp t τ
and for
ω s 2 + ω 2
is
f ( t ) = sin ω t
hence apply convolution theorem
0 t g ( v ) f ( t v ) d v
solve the integral you get the result
sengihantq

sengihantq

Beginner2022-10-07Added 3 answers

y ( x ) = e x / τ ω τ ω τ cos ( ω x ) + sin ( ω x ) 1 + ω 2 τ 2

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