Recent questions tagged laplace-transforms / GO Mechanical

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GATE Mechanical 2021 Set 2 | Question: 2
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$

If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is$0$$\frac{1}{2}$$1$$\frac{3}{2}$

go_editor

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go_editor asked Mar 1, 2021

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GATE Mechanical 2021 Set 1 | Question: 3
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$

The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$, has the following property$$\int_{a}^{b}\varphi \left ...

gatecse

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gatecse asked Feb 22, 2021

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GATE2020-ME-2: 4
The solution of $\dfrac{d^2y}{dt^2}-y=1,$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$

The solution of $$\dfrac{d^2y}{dt^2}-y=1,$$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is$\dfrac{1}...

go_editor

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go_editor asked Sep 18, 2020

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GATE2020-ME-1: 3
The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is $f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t \right ) \\$ $f\left ( t \right )=\dfrac{1}{\omega}\cos\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega}\sin\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega^{2}}\left ( 1-\sin\:\omega t \right )$

The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is$f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t ...

go_editor

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go_editor asked Feb 19, 2020

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GATE2019 ME-1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy-2x^2+2y^2+ \text{constant}$ $4y^2-4xy + \text{constant}$ $2x^2-2y^2+ xy + \text{constant}$ $-4xy+2y^2-2x^2+ \text{constant}$

A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is$4...

Arjun

28.5k points

Arjun asked Feb 9, 2019

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GATE2018-1-38
$F(s)$ is the Laplace transform of the function $f(t) =2t^2 e^{-t}$. $F(1)$ is _______ (correct to two decimal places).

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

Arjun

28.5k points

Arjun asked Feb 17, 2018

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GATE2017 ME-2: 5
The Laplace transform of $te^{t}$ is $\dfrac{s}{(s+1)^{2}} \\$ $\dfrac{1}{(s-1)^{2}} \\$ $\dfrac{1}{(s+1)^{2}} \\$ $\dfrac{s}{(s-1)}$

The Laplace transform of $te^{t}$ is$\dfrac{s}{(s+1)^{2}} \\$$\dfrac{1}{(s-1)^{2}} \\$$\dfrac{1}{(s+1)^{2}} \\$$\dfrac{s}{(s-1)}$

Arjun

28.5k points

Arjun asked Feb 26, 2017

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GATE2016-3-3
Solutions of Laplace’s equation having continuous second-order partial derivatives are called biharmonic functions harmonic functions conjugate harmonic functions error functions

Solutions of Laplace’s equation having continuous second-order partial derivatives are calledbiharmonic functionsharmonic functionsconjugate harmonic functionserror fun...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2016-2-3
Laplace transform of $\cos( \omega t)$ is $\dfrac{s}{s^2+\omega ^2} \\$ $\dfrac{\omega }{s^2+\omega ^2} \\$ $\dfrac{s}{s^2-\omega ^2} \\$ $\dfrac{\omega }{s^2-\omega ^2}$

Laplace transform of $\cos( \omega t)$ is$\dfrac{s}{s^2+\omega ^2} \\$$\dfrac{\omega }{s^2+\omega ^2} \\$$\dfrac{s}{s^2-\omega ^2} \\$$\dfrac{\omega }{s^2-\omega ^2}$

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2016-1-2
If $f(t)$ is a function defined for all $t \geq 0$, its Laplace transform $F(s)$ is defined as $\int_{0}^{\infty }e^{st}f(t)dt \\$ $\int_{0}^{\infty }e^{-st}f(t)dt \\$ $\int_{0}^{\infty }e^{ist}f(t)dt \\$ $\int_{0}^{\infty }e^{-ist}f(t)dt$

If $f(t)$ is a function defined for all $t \geq 0$, its Laplace transform $F(s)$ is defined as$\int_{0}^{\infty }e^{st}f(t)dt \\$$\int_{0}^{\infty }e^{-st}f(t)dt \\$$\int...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-3-44
Laplace transform of the function $f(t)$ is given by $F(s)=L\begin{bmatrix} f(t) \end{bmatrix}=\int_{0}^{\infty }f(t)e^{-st}dt$ . Laplace transform of the function shown below is given by $\displaystyle{\frac{1-e^{-2s}}{s}} \\$ $\displaystyle{\frac{1-e^{-s}}{2s}} \\$ $\displaystyle{\frac{2-2e^{-s}}{s}} \\$ $\displaystyle{\frac{1-2e^{-s}}{s}}$

Laplace transform of the function $f(t)$ is given by $F(s)=L\begin{bmatrix} f(t) \end{bmatrix}=\int_{0}^{\infty }f(t)e^{-st}dt$ . Laplace transform of the function shown ...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-2-4
The Laplace transform of $e^{i5t}$ where $i=\sqrt{-1}$, is $\dfrac{s-5i}{s^2-25} \\$ $\dfrac{s+5i}{s^2+25} \\$ $\dfrac{s+5i}{s^2-25} \\$ $\dfrac{s-5i}{s^2+25} $

The Laplace transform of $e^{i5t}$ where $i=\sqrt{-1}$, is$\dfrac{s-5i}{s^2-25} \\$$\dfrac{s+5i}{s^2+25} \\$$\dfrac{s+5i}{s^2-25} \\$$\dfrac{s-5i}{s^2+25} $

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | Question: 5
Laplace transform of $\cos(\omega t)$ is $\dfrac{s}{s^2+\omega ^2}$. The Laplace transform of $e^{-2t} \cos(4t)$ is $\dfrac{s-2}{(s-2)^2+16} \\$ $\dfrac{s+2}{(s-2)^2+16} \\$ $\dfrac{s-2}{(s+2)^2+16} \\$ $\dfrac{s+2}{(s+2)^2+16}$

Laplace transform of $\cos(\omega t)$ is $\dfrac{s}{s^2+\omega ^2}$. The Laplace transform of $e^{-2t} \cos(4t)$ is$\dfrac{s-2}{(s-2)^2+16} \\$$\dfrac{s+2}{(s-2)^2+16} \\...

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE ME 2013 | Question: 27
The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\dfrac{2}{s+1} \\$ $\dfrac{4}{s+1} \\$ $\dfrac{4}{s^2+1} \\$ $\dfrac{2}{s^4+1}$

The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform ...

piyag476

1.4k points

piyag476 asked Feb 19, 2017