Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
2) Given that p"(v) + 2p'(v) - 4p(v) = 8v

2) Given that p"(v) + 2p'(v) - 4p(v) = 8v

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Verify if my answers are correct
O Search (Alt+Q) ings Review Help ou need to edit, it's safer to stay in Protected View. to this PC V View 11. 1. 8+8² => P(s) = ²(s²+2s-4) 2 By decomposition we can write Cs+D s²-2s-4 2) Given that p"(v) + 2p'(v) - 4p(v) = 8v Taking Laplace transform we get (s²P(s) - sp(0) - p'(0)) + 2(sP(s) - p(0)) - 4P(s) = (s² +2s - 4)P(s) − 1 = => (s² + 2s - 4)P(s) = 8+² P(s) = A ++ => 8+ s² = As³ - 2As2-4As + Bs2 - 2Bs - 4B +Cs³ +Ds² => 8+ s² = s³(A+C) + s²(B - 2A + D) +(-4A - 2B)s - 4B So, we get P(s) = -2+2-3154 Step 3/3 Enable Editing ⇒A+C =0, B - 2A + D = 1,-4A - 2B = 0, -4B = 8 => B = -2, A = 1, C = -1,D = 5 As we get P(s) = ---- (51)²-5 + (8-1)²-5 Taking inverse Laplace we get p(v) = 1-2v- e'cos ((√5)v) + This is the Required I. 4e sin((√5)v) √5 4 5 A
Transcribed Image Text:O Search (Alt+Q) ings Review Help ou need to edit, it's safer to stay in Protected View. to this PC V View 11. 1. 8+8² => P(s) = ²(s²+2s-4) 2 By decomposition we can write Cs+D s²-2s-4 2) Given that p"(v) + 2p'(v) - 4p(v) = 8v Taking Laplace transform we get (s²P(s) - sp(0) - p'(0)) + 2(sP(s) - p(0)) - 4P(s) = (s² +2s - 4)P(s) − 1 = => (s² + 2s - 4)P(s) = 8+² P(s) = A ++ => 8+ s² = As³ - 2As2-4As + Bs2 - 2Bs - 4B +Cs³ +Ds² => 8+ s² = s³(A+C) + s²(B - 2A + D) +(-4A - 2B)s - 4B So, we get P(s) = -2+2-3154 Step 3/3 Enable Editing ⇒A+C =0, B - 2A + D = 1,-4A - 2B = 0, -4B = 8 => B = -2, A = 1, C = -1,D = 5 As we get P(s) = ---- (51)²-5 + (8-1)²-5 Taking inverse Laplace we get p(v) = 1-2v- e'cos ((√5)v) + This is the Required I. 4e sin((√5)v) √5 4 5 A
Mailings Review View Help Unless you need to edit, it's safer to stay in Protected View. T I T 1 1 => G(s) — * S (³) G(s) = 8² 149 s2 + 30+ = 1 49 => C= 147 58 1 Given function is g(t)-3g(u)du = cos (7t) Taking Laplace transform we get L-¹(g(t)) — 3L ¹(ſ'g(u)du) = L−¹(cos (7t)) 3G(s) S B = ⇒ B= 49 58 So, we get G(s) = 9 I => G(s) = (s−3)(s² | 49) Using partial decomposition we can write Bs + C G(s) = 3 58(s-3) A = 1-B⇒ A= 8 9 S s²49 + . 9 => G(s) = 58(8-3) S²49 => s² = A (s² +49) + (Bs + C)(s − 3) => s² = s² (A + B) + s(C − 3B) + (49A — 3C) A+B=1 C-3B = 0 ⇒ B= 49A3C = 0⇒ A= 3C 49 K + 2 49s-+-147 s²1-49 49s s²149 1 + Taking inverse Laplace we get 9e3t g(t) 58 I 147 s² +49 1 +49cos (7t) + 21sin (7t) 3 E Enable Ed | F
Transcribed Image Text:Mailings Review View Help Unless you need to edit, it's safer to stay in Protected View. T I T 1 1 => G(s) — * S (³) G(s) = 8² 149 s2 + 30+ = 1 49 => C= 147 58 1 Given function is g(t)-3g(u)du = cos (7t) Taking Laplace transform we get L-¹(g(t)) — 3L ¹(ſ'g(u)du) = L−¹(cos (7t)) 3G(s) S B = ⇒ B= 49 58 So, we get G(s) = 9 I => G(s) = (s−3)(s² | 49) Using partial decomposition we can write Bs + C G(s) = 3 58(s-3) A = 1-B⇒ A= 8 9 S s²49 + . 9 => G(s) = 58(8-3) S²49 => s² = A (s² +49) + (Bs + C)(s − 3) => s² = s² (A + B) + s(C − 3B) + (49A — 3C) A+B=1 C-3B = 0 ⇒ B= 49A3C = 0⇒ A= 3C 49 K + 2 49s-+-147 s²1-49 49s s²149 1 + Taking inverse Laplace we get 9e3t g(t) 58 I 147 s² +49 1 +49cos (7t) + 21sin (7t) 3 E Enable Ed | F
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS