please explain how to do number 3 clearly. Question 3For the same differential equation as in Problem 1:* + 2a + 25 x = 25 v (t), with x (0)Let a = 13. Calculate the zero-input response(external input v (t) = 0)Oz-i (t) = 8e-13t3e-25tOz-i(t) = 4e-13t cos (5t) + e-5tO 5e-13t cos (5t), t≥ 0O 2z-i(t) 4 et + e-25t""t≥ 0t≥ 0"x (0) = 5, * (0)t≥ 0= - 29z-i (t) for t≥ 0 Question 1da(t)* (t) =dt "dt²Consider the following differential equation:* (t) =+ 2a + 25 x ==x (0)5, * (0)Let the external input be zero. Write the Laplace transform of the zero-input-response z-i (t),i.e., X₂-i (8) L{xi(t)} in terms of the given initial conditions and a(Note: All given initial conditions are just before t = 0, i.e.,x (0), * (0) = (0_ ) in all problems).=O X₂-i (8)Cannot be determined with the given information.O X₂-i (8)O X-i (s)=25 v (t) with initial conditions:= - 29===2582 +2 as+25a 5s²+2 as+255 (8+2a) - 2982 +2a 8+25

Introduction Zero state response The zero state response (ZSR), in the theory of electrical…

Question 3 For the same differential equation as in Problem 1: * + 2a + 25 x = 25v (t), with x (0) = 5, * (0) = Let a = 13. Calculate the zero-input response -i (t) for t≥ 0 (external input v (t) = 0) O2z-i(t) 8e-13t Oz-i(t) = 4e-13t cos (5t) + e-st t≥ 0 O 5e-13t cos (5t), t≥ 0 O 2z-i(t) = 4 et + e-25 t " 3 e 25t " t≥0 t≥0 - 29 "

Question 3 For the same differential equation as in Problem 1: * + 2a + 25 x = 25v (t), with x (0) = 5, * (0) = Let a = 13. Calculate the zero-input response -i (t) for t≥ 0 (external input v (t) = 0) O2z-i(t) 8e-13t Oz-i(t) = 4e-13t cos (5t) + e-st t≥ 0 O 5e-13t cos (5t), t≥ 0 O 2z-i(t) = 4 et + e-25 t " 3 e 25t " t≥0 t≥0 - 29 "

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

I need help with the question below Consider a causal linear-time invariant system described by the differential equation 2y′(t) + 6y(t) = x′(t) − 4x(t)1. Using Laplace transform technique, determine the zero-input response yz (t) if y(0−) = -3. Assume x(0−) and its higher order derivative in the vicinity of t = 0 to be zero.2. Using the Laplace transform technique, determine the zero-state response if x(t) = δ(t − π)
a. laplace transform of DE b.simplified algebraic expression of the laplace transformation by equating it in terms of its dependent variable, (I(s)). c. inverse laplace transform of each factor of the denominator of the laplace algebraic expession by using the Heaviside Expansion Theorems. D. WRITE THE DIFFERENTIAL EQUATION, i(t), using HET( where; i(t)=i^1(t) +i^2(t)+i^3(t)...).
I need help with the question below. 1. By the direct integration, i.e. using the formula of Laplace transform, find the Laplace transform of (i) 2u(t) − 2u(t − 1), (ii) te^−(2t)u(t).2. Also, state their region of convergence. 3. Sketch both of the signals.
the following statements given, write if each statement is true or false. a. If the complex frequency domain function, F(s), is derived using a “One-sided” Laplace Transform, the inverse of that function, f(t), is only valid for t ≥ 0. b. When using an ideal transformer, if voltage increases from primary side to secondary side, current also increases from primary side to the secondary side. c. Initial value theorem states that the initial value of a time function f(t) can be obtained from its Laplace Transform F(s) by multiplying the transform by s and letting s approach zero. ..
Derive the s-domain equivalent circuit by expressing the inductor current i as a function of the terminal voltage v and then finding the Laplace transform of this time-domain integral equation.
Problem 5. Which gives the Laplace transforms of the given time-domain function? ln [(s + sqrt 2)/(s - sqrt 5)] ln [(s - sqrt 2)/(s + sqrt 5)] ln [(s - 2)/(s + 5)] ln [(s - sqrt 2)(s + sqrt 5)]
TRUE OR FALSE 1. The Laplace transform of two functions is equal. The functions are equal. 2. Laplace transform is a linear operator. 3. The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero. 4. L(f*g) = L(f).L(g). 5. Every function f(t) has a Laplace transform. 6. Taking the inverse Laplace transform gives us a function that is in the time domain. 7. Inverse Laplace transform is a linear operator. 8. The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function. 9. If the denominator of a Laplace transform has degree 4, you should expect to find 4 items in the table to use for writing the transform as a sum of terms. 10. L(f(t)/t) = -F’(s). 11. L(3y+5w)=3∙L(y)+5∙L(w). 12. Daniel Bernoulli is the original author of Laplace Transform. 13. The Laplace transform of the sum of two functions is equal to the sum of the…
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 ?
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) will be ?
i)determine laplace transform of signal x(t) in fig q1(a) and state its region of convergence ii)determine laplace transform of e^3t x(t)
Taking the inverse Laplace transform gives us a function that is in the time domain. Select one: True False The transfer function is the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all initial conditions equal to zero. Select one: True False L(f(t)/t) = -F’(s). Select one: True False If the denominator of a Laplace transform has degree 4, you should expect to find 4 items in the table to use for writing the transform as a sum of terms. Select one: True False Laplace transform is a linear operator. Select one: True False The Laplace transform of two functions is equal. The functions are equal. Select one: True False Daniel Bernoulli is the original author of Laplace Transform. Select one: True False Inverse Laplace transform is a linear operator. Select one: True False L(f*g) = L(f).L(g). Select one: True False The Laplace transform of the sum of two functions is equal to the sum of…
In the following circuit, R=1 [ohm], C=1[F], and all initial values are 0. 1. Using Laplace Transform, find the ratio H(s)=Vo(s)/Vi(s).2. Find the roots of the characteristic equation.3. Find the conditions for K which will make the circuit over-damped and under-damped, respectively.4. When K=2, vi(t)=sqrt(10)cost, find vo(t) after a long time has passed.