Question

Q1.find laplace transformation of

cos3t​

Answer 1

Step-by-step explanation:

Answer:

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

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

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:

$</p><p>\begin{gathered}\implies L(\:Cos(3t)\:) = \dfrac{s}{s^2 + 3^2}\\\\\\\boxed{ \bf{ \implies L(\:Cos(3t)\:) = \dfrac{s}{s^2 + 9}}}\end{gathered} </p><p>$

This is the required answer.

Answer 2

Answer:

At the most fundamental level, matter is composed of elementary particles known as quarks and leptons (the class of elementary particles that includes electrons). ... The three most familiar forms, or states, of matter are solid, liquid, and gas. Heating and cooling a substance may change it from one state to another.