Question (a)
The Inverse Laplace Transform is
Using
So
We get
So the Inverse is
The right sided sequence is
The left sided sequence is
Question (b)
The function is not causal as the present value depends on the future inputs
For example, the output at time t = -2
So the output at time t = -2 depends on the input at t = 2. So the function is not causal
8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the...
Signal and Systems 8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the ROC is defined as: -12 <Re(s) <0 Identify terms as right sided or left sided. S+12 Re(s) < 0 Re(s) >-12 Х X -12 0 Problem 1b (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why:
12 Problem la (10 points) Find the inverse Laplace transform of: Fo(s) the ROC is defined as: -12 < Re(s) <0 Identify terms as right sided or left sided. 8 +- If S S+12 Re(s)< 0 Re(s) >-12 X X -12 0 Problem lb (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why: Given the unilateral Laplace transform of the impulse response for a causal system H(S) = Determine h(t) the impulse response? Hint synthetic...
Laplace Transform 12 12 + s+12 s+8 Problem 4 (15 points) : Find the inverse Laplace transform of: Fo(s) a) If the ROC is defined as: -12 < Re(s)<-8 b) If the ROC is defined as: Re(s) > -8
Find the inverse Laplace transform, f(t) of the 10 3 10 function F(s) + + s > 0 S 52 s + 10 f(t) = Preview t > 0 Submit License Question 2. Points possible: 2 Unlimited attempts. Message instructor about this question
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Signal and Systems Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...
Thank you! Chapter 13, Problem 13.35 (Circuit Solution) Find the inverse Laplace transform of the following functions. (a) F(s) -8 S+ 6 (b) F(s) - e (c) F(s)-1-e-6s S + 8 (a) Find ft) (inverse Laplace transform) at t = 9. (b) Find f(t) (inverse Laplace transform) at t = 3. (c) Find f(t) (inverse Laplace transform) at t7. ) (inverse Laplace transform) a
Laplace Transform Problem 1: Concept Questions, Provide a short succinct answer to each question or circle the correct answer a) (3 points) You need to find the bilateral Laplace transform for f-(t) = cos(-bt) u(-t). Using the process shown in class to find bilateral transform from a unilateral table, which one of the following is the correct expression for F5 (s) and its ROC a. Fb (s) = S S2+b Re(s) > 0 b. F5 (s) = S s2+b shib...
1. (10 points) Find the inverse Laplace transform of the following: 85 - 4s +12 s? +45-5 b. F(x) = s(s? +2s + 5) 2. (10 points) Determine if the following differential equation is exact. Be sure give a reason for why or why not. If it is exact, solve it. (xy? + 3x y)+(x° +xºy)y'=0 a. F(s)= (1-25)e-
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...