Need do a Laplace transformation for T_1 * V′(t)+V(t)=K * P(t)+Va

Jackson Garner 2022-09-24 Answered
I am trying to do a Laplace transform of the following equation:
T1⋅V′(t)+V(t)=K⋅P(t)+Va
The purpose is to solve V(s) equation knowing that V(0)=Va. I followed all the transformation rules and I got the following result:
V(s)=K⋅P(s)s⋅(1+T1)+Vas
But, according to the correction, the expected result is :
V(s)=K⋅P(s)(1+s⋅T1)+Vas
What have I done wrong?
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Answers (1)

Solomon Fernandez
Answered 2022-09-25 Author has 5 answers
T 1 V ( t ) + V ( t ) = K P ( t ) + V a
Apply Laplace Transform:
T 1 ( s V ( s ) V ( 0 ) ) + V ( s ) = K P ( S ) + V a s
V ( s ) ( s T 1 + 1 ) = K P ( S ) + V a s + T 1 V ( 0 )
Since V ( 0 ) = V a we have:
V ( s ) ( s T 1 + 1 ) = K P ( S ) + V a s + T 1 V a
V ( s ) ( s T 1 + 1 ) = K P ( S ) + V a ( 1 + s T 1 ) s
It finally gives:
V ( s ) = K P ( S ) ( s T 1 + 1 ) + V a s
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