Question

find laplace transformation of

cos3t​

Answer 1

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.