GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 60 of 65

Marks: +1, -0

F(s)

is the Laplace transform of the function

f(t)=2 t^{2} e^{-t}

{F}(1)

is ______________(correct to two decimal places).

Solution:

L(t^{n})=\;{n !}/{s^{n+1}}

L(t^{2})=\;{2 !}/{s^{2+1}}=\;{2}/{s^{3}}

L(2 t^{2})=2 L(t^{2})=\;{4}/{s^{3}}

L(2 t^{2} e^{-α t})=\;{4}/{(s+α)^{3}}

L(2 t^{2} e^{-t})=\;{4}/{(s+1)^{3}}=F(s)

Hence

F(1)=\;{4}/{2^{3}}=0.5

Go to Question:

Prev Question

Next Question