PYQs Based Test - 13 : Laplace Transforms

The Laplace transform of sin h (at) is

The function f(t) satisfies the differential equation $\frac{d^{2}f}{d{t}^2}+f=0$ and the auxiliary conditions, $f\left(0\right)=0,\frac{df}{dt}\left(0\right)=4$ . The Laplace transform of f(t) is given by

F(s) is the Laplace transform of the function

f(t) = 2t²e${}^{-t}$

F (1) is ________ (correct to two decimal places).

Laplace transform of the function f(t) is given by $F\left(s\right)=L\left\{f\left(t\right)\right\}=\underset{0}{\overset{\infty }{\int }}f\left(t\right)e^{-st}dt$. Laplace transform of the function shown below is given by

The inverse Laplace transform of $H\left(s\right)=\frac{s+3}{s^2+2s+1}$ for t ≥ 0 is