Chapter 13, Problem 1P

If the Laplace transform of f(t) is given by   then f(0) is

Consider the following cases where we want to determine different types of responses. (a) The input to a LTI system is x(t)= u(t) − 2u(t − 1) + u(t − 2)and the Laplace transform of the output is given by Y(s) = [(s+2)(1-e^(-s))^2]/[s(s+1)^2]. Determine the impulse response of the system. (b) Without computing the inverse of the Laplace transform X(s) = 1/[s(s^2+2s+10)] corresponding to a causal signal x(t), determine limt→∞x(t). (c) The Laplace transform of the output of a LTI system is Z(s) = 1/[s((s+2)^2+1)], what would be the steady-state response zss(t)? (d) The Laplace transform of the output of a LTI system is W(s) = e^(-s)/[s((s-2)^2+1)], how would you determine if there is a steady state or not? Explain. (e) The Laplace transform of the output of a LTI system is V(s) = (s+1)/[s((s+1)^2+1)]. Determine the steady state and the transient responses corresponding to V(s).

The Laplace transform of the output of an LTI system is Y(s)=1/(s+3). Find out the expression of y(t)

Consider the function, F(s) = 5/s(s2+3s+2) where F(s) is the Laplace transform of the function f(t). The initial value of f(t) is equal to ?

A system with an impulse response of h(t) = e(-t/2) is driven by a forcing function x(t)=1-u(t-1). Determine the time domain output response y(t) using: a) Time-domain convolutional integral b) The Laplace transform and the inverse Laplace transform

The transfer function of a system is given as follows:A)permanent status error find ESSB)Perform the Inverse Laplace transformation of Y(s)C)graph of the time-dependent change of y (t)draw and show that the ESS you found are correct.

Derive the Laplace transform of a test signal

Consider a Laplace transform F(s) = 2(s + 1)/(s^2 + 4s + 7). Determine the initial value and final value of f(t).

Sketch or graph the given function, which is assumed to be zero outside the given interval. Represent it, using unit step functions. Find its Laplace transform using the second shifting theorem. t(0<t<2)