laplace-transform

Let f(t) be a function of t defined for all positive values of t. The Laplace transform of f(t) denoted by L{f(t)} = ∫₀^∞ e^(-st)f(t)dt, provided that the integral exists where s i...

Which one of the options given is the inverse Laplace transform of $\frac{1}{s^3-s}$? u(t) denotes the unit-step function.

If the Laplace transform of a function f(t) is given by (s+3)/((s+1)(s+2)), then f(0) is

The Dirac-delta function ($\delta(t - t_0)$) for $t, t_0 \in \mathbb{R}$, has the following property $\int_a^b \varphi(t)\delta(t - t_0)dt = \begin{cases} \varphi(t_0) & a 0$; $\ma...

The Laplace transform of $te^t$ is

$F(s)$ is the Laplace transform of the function $f(t) = 2t^2e^{-t}$. $F(1)$ is ________ (correct to two decimal places).

The Laplace Transform of $$f\left( t \right) = {e^{2t}}\sin \left( {5t} \right)\,u\left( t \right)$$ is

The Laplace transform of $${e^{i5t}}$$ where $$i = \sqrt { - 1} ,$$

Laplace transform of $$\cos \left( {\omega t} \right)$$ is

Laplace transform of $$\cos \,\left( {\omega t} \right)$$ is $${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transform of $${e^{ - 2t}}\,\cos \left( {4t} \right)$$ is

The function $$f(t)$$ satisfies the differential equation $${{{d^2}f} \over {d{t^2}}} + f = 0$$ and the auxiliary conditions, $$f\left( 0 \right) = 0,\,{{df} \over {dt}}\left( 0 \r...

The Laplace transform of $$f\left( t \right)$$ is $${1 \over {{s^2}\left( {s + 1} \right)}}.$$ The function

If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace transform of $$\int\limits_0^t {f\left( x \right)dx} $$ is

Laplace transform of $${\left( {a + bt} \right)^2}$$ where $$'a'$$ and $$'b'$$ are constants is given by:

Solve the initial value problem $${{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 3y = 0$$ with $$y=3$$ and $${{dy} \over {dx}} = 7$$ at $$x=0$$ using the laplace transform techni...

If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by $$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for...