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For the same differential equation as in Problem 1: * + 2a + 25 x = 25 v (t) Find the condition on a so that the zero-input response is overdamped. 0 a 70 0a>5 Ο α Σ ν 25 O a ≥ 25

For the same differential equation as in Problem 1: * + 2a + 25 x = 25 v (t) Find the condition on a so that the zero-input response is overdamped. 0 a 70 0a>5 Ο α Σ ν 25 O a ≥ 25

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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please help and clearly explain number 2. How would I find critical and underdamped?

 

Question 2 For the same differential equation as in Problem 1: * + 2a + 25 x 25 v (t) Find the condition on a so that the zero-input response is overdamped. ○a #0 a> 5 a > ν 25 O a ≥ 25 =
Transcribed Image Text:Question 2 For the same differential equation as in Problem 1: * + 2a + 25 x 25 v (t) Find the condition on a so that the zero-input response is overdamped. ○a #0 a> 5 a > ν 25 O a ≥ 25 =
Question 1 dx (t) * (t) dt Consider the following differential equation: 25 v (t) * + 2a + 25 x = 9 O Xz-i (s) x (0) = 5, * (0) Let the external input be zero. Write the Laplace transform of the zero-input-response xz-i (t), i.e., Xz-i (s) L{xi (t)} in terms of the given initial conditions and a O Xz-i (s) * (t) = = (Note: All given initial conditions are just before t = 0, i.e., x (0) x (0), * (0) * (0_ ) in all problems). = = O Cannot be determined with the given information. O Xz-i (s) = d² x(t) dt² = - 29 25 with initial conditions: s²+2 as+25 a 5 82 +2 as+25 5 (8+2a) - 29 s2+2 as+25
Transcribed Image Text:Question 1 dx (t) * (t) dt Consider the following differential equation: 25 v (t) * + 2a + 25 x = 9 O Xz-i (s) x (0) = 5, * (0) Let the external input be zero. Write the Laplace transform of the zero-input-response xz-i (t), i.e., Xz-i (s) L{xi (t)} in terms of the given initial conditions and a O Xz-i (s) * (t) = = (Note: All given initial conditions are just before t = 0, i.e., x (0) x (0), * (0) * (0_ ) in all problems). = = O Cannot be determined with the given information. O Xz-i (s) = d² x(t) dt² = - 29 25 with initial conditions: s²+2 as+25 a 5 82 +2 as+25 5 (8+2a) - 29 s2+2 as+25
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