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)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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please explain how to do number 3 clearly.

Transcribed Image Text:Question 3
For 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-13t
3e-25t
Oz-i(t) = 4e-13t cos (5t) + e-5t
O 5e-13t cos (5t), t≥ 0
O 2z-i(t) 4 et + e-25t
"
"
t≥ 0
t≥ 0
"
x (0) = 5, * (0)
t≥ 0
= - 29
z-i (t) for t≥ 0

Transcribed Image Text:Question 1
da(t)
* (t) =
dt "
dt²
Consider 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
=
=
=
25
82 +2 as+25
a 5
s²+2 as+25
5 (8+2a) - 29
82 +2a 8+25
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