Questions & Answers of Definitions and properties of Laplace transform

Question No. 40

The Laplace transform of the causal periodic square wave of period T shown in the figure below is

 

Question No. 240

A signal $2\cos\left(\frac{2\mathrm\pi}3t\right)-\;\cos\;\left(\mathrm{πt}\right)$ is the input to an LTI system with the transfer function

                                                                          $H\left(s\right)=e^s+e^{-s}$

If Ck denotes the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to

Question No. 111

The bilateral Laplace transform of a function ft=1if atb0Other wise is

Question No. 127

Let the signal f(t) = 0 outside the interval [T1, T2], where T1 and T2 are finite. Furthermore, ft< . The region of convergence (RoC) of the signal’s bilateral Laplace transform F(s) is

Question No. 136

Consider the differential equation dxdt = 10-0.2x with initial condition x(0) = 1. The response x(t) for t>0 is

Question No. 153

Input x(t) and output y(t) of an LTI system are related by the differential equation y''(t) - y-(t) - 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

Question No. 155

Let x(t) = α s(t) +s(–t) with s(t) = βe-4t u(t) , where u(t) is unit step function . If the bilateral Laplace transform of x(t) is

Xs = 16s2- 16-4 <Re{s}<4;

Then the value of β is______.

Question No. 55

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system

y.t+5yt=ut

When y(0) =1 and u(t) is a unit step function, y(t) is

Question No. 33

The impulse response of a continuous time system is given by h(t) = δ(t -1) + δ(t - 3) . The value of the step response at t = 2 is

Question No. 36

A system is described by the differential equation d 2 y d t 2 + 5 d y d t + 6 y ( t ) = x ( t ) .
Let x(t) be a rectangular pulse given by
x ( t ) = { 1 0 < t < 2 0 o t h e r w i s e

Assuming that y(0) = 0 and d y d t = 0 at t = 0, the Laplace transform of y(t) is

Question No. 11

The unilateral Laplace transform of f (t) is 1s2+s+1. The unilateral Laplace transform of t f (t) is

Question No. 18

If the unit step response of a network is 1-e-αt then its unit impulse response is

Question No. 43

An input x (t) = exp (−2t)u(t) + δ (t − 6) is applied to an LTI system with impulse response h(t) = u(t) . The output is is

Question No. 45

If FS=L[ft]=2s+1s2+4s+7  then the initial and final values of f(t) are respectively

Question No. 41

A continuous time LTI system is described by

d2ytdt2+4dytdt+3yt=2dxtdt+4xt

Assuming zero initial conditions, the response y(t) of the above system for the input x(t)=e-2t u(t) is given by

Question No. 24

Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $\style{font-size:14px}{\int\limits_0^tf\left(\tau\right)\operatorname{d}\tau}$ is

Question No. 16

If the Laplace transform of a signal y(t) is Ys=1ss-1, then its final value is