Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]
Consider the damped forced motion described by d'y c dy di? k Fo cos ot. |- m dt m m We have shown that the steady-state solution can be written in the form Fo cos(ot – v), H Yp(t) = where m(w – o?) со sin v = H COS V = H k m H = /m2(03 – 0²)2 + c?w?. Assuming that c2/(2m²w}) < 1, show that the ampli- tude of the steady-state solution is a maximum when c2 0 = 2m2 [Hint: The maximum occurs at the value of w that makes H a minimum. Assume that H is a function of w, and determine the value of w that minimizes H.]
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Consider the damped forced motion described by
d'y c dy
di?
k
Fo
cos ot.
|-
m dt
m
m
We have shown that the steady-state solution can be
written in the form
Fo
cos(ot – v),
H
Yp(t) =
where
m(w – o?)
со
sin v =
H
COS V =
H
k
m
H = /m2(03 – 0²)2 + c?w?.
Assuming that c2/(2m²w}) < 1, show that the ampli-
tude of the steady-state solution is a maximum when
c2
0 =
2m2
[Hint: The maximum occurs at the value of w that
makes H a minimum. Assume that H is a function of
w, and determine the value of w that minimizes H.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8710dbee-149c-4b1a-ad34-ec526b6df74a%2Fe85bc3a3-a8a2-4263-a08e-a8ee0ad2374a%2F4nxuxh.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the damped forced motion described by
d'y c dy
di?
k
Fo
cos ot.
|-
m dt
m
m
We have shown that the steady-state solution can be
written in the form
Fo
cos(ot – v),
H
Yp(t) =
where
m(w – o?)
со
sin v =
H
COS V =
H
k
m
H = /m2(03 – 0²)2 + c?w?.
Assuming that c2/(2m²w}) < 1, show that the ampli-
tude of the steady-state solution is a maximum when
c2
0 =
2m2
[Hint: The maximum occurs at the value of w that
makes H a minimum. Assume that H is a function of
w, and determine the value of w that minimizes H.]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY