Recent questions tagged laplace-transform

Given two signals: $x(t)=u(t-2)-u(t-3)$, and $y(t)=e^{-4 t} u(t)$. If $z(t)=x(t) * y(t)$, then $Z(s)$ is $\_\_\_\_$.$\dfrac{e^{-3 s}\left[e^{s}-1\right]}{s(s+4)}$$\dfrac{...

​​​​​Laplace transform of a signal $x(t)$ is$$X(s)=\frac{1}{s^{2}+13 s+42}$$Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if t...

The Laplace transform of the continuous-time signal $x(t)=e^{-3 t} u(t-5)$ is_____________, where $u(t)$ denotes the continuous-time unit step signal.$\frac{e^{-5 s}}{s+3...

The signal $x(t) = (t-1)^{2}u(t-1),$ where $u(t)$ is the unit-step function, has the Laplace transform $X(s).$ The value of $X(1)$ is ________$\frac{1}{e}$$\frac{2}{e}$$2...

Let $u\left ( t \right )$ denote the unit step function. The bilateral Laplace transform of the function $f\left ( t \right )=e^{t}u\left ( -t \right )$ is ______________...

The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.

The transfer function relating the input x(t) to the output y(t) of a system is given by G(s) = 1/(s + 3). A unit-step input is applied to the system at time t = 0. Assum...

If $X(s)$, the Laplace transform of signal $x(t)$ is given by $X(s) = \frac{(s+2)}{(s+1)(s+3)^2}$, then the value of $x(t)$ as $t\rightarrow \infty$ is ______.

The relationship between the force $f(t)$ and the displacement $x(t)$ of a spring-mass system (with a mass $M$, viscous damping $D$ and spring constant $K$) is$$M\frac{d^...

The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$$...

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...