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Recent questions tagged laplace-transform
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GATE ECE 2016 Set 1 | Question: 4
Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$? The solutions have neither maxima nor minima anywhere except at the boundaries. The solutions are not separable in the coordinates. The solutions are not continuous. The solutions are not dependent on the boundary conditions.
Milicevic3306
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Network Solution Methods
Mar 28, 2018
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Milicevic3306
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gate2016-ec-1
network-solution-methods
laplace-transform
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GATE ECE 2016 Set 1 | Question: 30
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{-sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{-sT/2})} \\$ $F(S) = \frac{1}{s(1-e^{-sT})} \\$ $F(S) = \frac{1}{1-e^{-sT}}$
Milicevic3306
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Network Solution Methods
Mar 28, 2018
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Milicevic3306
15.8k
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76
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gate2016-ec-1
network-solution-methods
laplace-transform
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3
GATE ECE 2015 Set 2 | Question: 1
The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is $\dfrac{a-b}{s} \\$ $\dfrac{e^{s}(a-b)}{s} \\$ $\dfrac{e^{-as}-e^{-bs}}{s} \\$ $\dfrac{e^{s(a-b)}}{s}$
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Network Solution Methods
Mar 28, 2018
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Milicevic3306
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gate2015-ec-2
network-solution-methods
laplace-transform
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4
GATE ECE 2015 Set 2 | Question: 17
Let the signal ݂$f(t) = 0$ outside the interval $[T_{1},T_{2}]$, where ܶ$T_{1}$ and ܶ$T_{2}$ are finite. Furthermore, $\mid f(t) \mid < \infty$ ... ݆$j\Omega$ axis a parallel strip not containing the ݆$j\Omega$ axis the entire $s$- plane a half plane containing the ݆$j\Omega$ axis
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Network Solution Methods
Mar 28, 2018
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Milicevic3306
15.8k
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75
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gate2015-ec-2
network-solution-methods
laplace-transform
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5
GATE ECE 2015 Set 2 | Question: 45
Let $x(t) = \alpha s(t) + s(-t)$ with $s(t) = \beta e^{-4t}u(t),$ where $u(t)$ is unit step function. If the bilateral Laplace transform of $x(t)$ is $X(s) = \dfrac{16}{s^{2} – 16}\:\: -4 < Re\{s\}<4;$ then the value of $\beta$ is ______.
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Network Solution Methods
Mar 28, 2018
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Milicevic3306
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gate2015-ec-2
numerical-answers
network-solution-methods
laplace-transform
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6
GATE ECE 2014 Set 4 | Question: 28
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. Which one of the following is the unilateral Laplace transform of $g(t) = t \cdot f(t)$? $\frac{-s}{(s^2+s+1)^2}$ $\frac{-(2s+1)}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
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Network Solution Methods
Mar 26, 2018
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Milicevic3306
15.8k
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55
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gate2014-ec-4
network-solution-methods
laplace-transform
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7
GATE ECE 2013 | Question: 36
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ ... $\frac{e^{-2s}}{(s+2)(s+3)} \\$ $\frac{1-e^{-2s}}{s(s+2)(s+3)} $
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Differential Equations
Mar 26, 2018
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Milicevic3306
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50
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gate2013-ec
differential-equations
laplace-transform
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8
GATE ECE 2012 | Question: 11
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}$. The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
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Network Solution Methods
Mar 25, 2018
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Milicevic3306
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59
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gate2012-ec
network-solution-methods
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