Math, asked by simrankumari6584, 9 months ago

find laplace transformation of

cos3t​

Answers

Answered by Steph0303
17

Answer:

Laplace Transform of any function f(t) is given as:

\boxed{ \bf{ L(f(t)) = \int\limits^\infty_0 {e^{-st}.f(t)} \, dt }}

Laplace Transform of f(t) = Cos(at) is given as:

\implies L(\:Cos(at)\:) = \dfrac{s}{(s^2+a^2)} \hspace{10}...(1)

According to the question, we are required to find the value of Cos(3t).

Comparing it with the general form we get:

⇒ a = 3

Substituting the value of 'a' in Eqn. (1) we get:

\implies L(\:Cos(3t)\:) = \dfrac{s}{s^2 + 3^2}\\\\\\\boxed{ \bf{ \implies L(\:Cos(3t)\:) = \dfrac{s}{s^2 + 9}}}

This is the required answer.

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