Undamped oscillators that are driven at resonance have unusual (and nonphysical) solutions. To investigate this, complete parts (a) through (e) below. (a) Find the synchronous solution Acos S2t + Bsin 2: to the generic forced oscillator equation my" + by' + ky = cos 1t. y(l) = cos C1 + V sin S2t. (b) Sketch graphs of the coefficients A and B, as functions of 2. for m = 1, b= 0.1, and k = 25. Choose the correct graph below. O A. OB. Oc. OD. 1.5 1.5 A 2.5 2.5 2.5 2.5 IB 1.5 1.5 B. (c) Now set b=0 in your formulas for A and Band resketch the graphs in part (b), with m= 1. and k= 25. What happens at 2= 5? Notice that the armplitudes of the syrchronous solutions grow without bound as 2 approaches 5. Choose the correct graph below. OA. OB. Oc. OD. 4- 4- 4- A B A A

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
icon
Related questions
Question

Sub- Mechanical vibrations 

 

What happens at 2=5?
O A. The uridarriped oscillator ostillates at a constant frequericy indelinitely.
O B. The trequency of the oscillations becomes unbounded.
OC. The undamped oscillator stretches indefinitely.
OD. The amplitude of the oscillations becomes unbounded.
(d) Show directly, by substituting the form Acos 2: - Bsin 12t Into the equation my" + by' + ky = cos (2t, that when b=0 there are no aynchronous solutions if 12 =
Select the correct cholce below and, if neceasary, fill in the anawer box within your
chcice.
OA.
Substituting b= 0 and 2=
m
Into the coefficients A and Band simplifylng results in the equation which has no solution.
OB.
Substituting b=0 and 2=
into the cocfficients A and B and simplifying results in civision by 0.
k
tsin r solves the equation my' + by' + ky = cos t when b= 0 and 2= . Notice that this nonsynchronous solution grows in time, without bound.
(e) Verlty that (2m2)
- [2mA :sin . Fnd y't
After substituting
for 2, the given differential equation will be of the form my" + ky = cos =tand the solution will be of the form y(t) =
What is observed in the simplification process after insertion of y"(t) and y(t) into the differential equation my" + ky = cos
m
The term in y"(t) cancels out, resulting in the equation cos
t= cos
t, thus completing the verification.
Transcribed Image Text:What happens at 2=5? O A. The uridarriped oscillator ostillates at a constant frequericy indelinitely. O B. The trequency of the oscillations becomes unbounded. OC. The undamped oscillator stretches indefinitely. OD. The amplitude of the oscillations becomes unbounded. (d) Show directly, by substituting the form Acos 2: - Bsin 12t Into the equation my" + by' + ky = cos (2t, that when b=0 there are no aynchronous solutions if 12 = Select the correct cholce below and, if neceasary, fill in the anawer box within your chcice. OA. Substituting b= 0 and 2= m Into the coefficients A and Band simplifylng results in the equation which has no solution. OB. Substituting b=0 and 2= into the cocfficients A and B and simplifying results in civision by 0. k tsin r solves the equation my' + by' + ky = cos t when b= 0 and 2= . Notice that this nonsynchronous solution grows in time, without bound. (e) Verlty that (2m2) - [2mA :sin . Fnd y't After substituting for 2, the given differential equation will be of the form my" + ky = cos =tand the solution will be of the form y(t) = What is observed in the simplification process after insertion of y"(t) and y(t) into the differential equation my" + ky = cos m The term in y"(t) cancels out, resulting in the equation cos t= cos t, thus completing the verification.
Undamped oscillators that are driven at resonance have unusual (and nonphysical) solutions. To investigate this, complete parts (a) through (e) below.
(a) Find the synchronous solution Acos S2t + Bsin 2: to the generic forced oscillator equation my" + by' + ky = cos 1t.
y(l) =
cos C1 +
V sin S2t.
(b) Sketch graphs of the coefficients A and B, as functions of 2. for m = 1, b= 0.1, and k = 25. Choose the correct graph below.
O A.
OB.
Oc.
OD.
1.5
1.5
A
2.5
2.5
2.5
2.5
IB
1.5
1.5
B.
(c) Now set b=0 in your formulas for A and Band resketch the graphs in part (b), with m= 1. and k= 25. What happens at 2= 5? Notice that the armplitudes of the syrchronous solutions grow without bound as 2 approaches 5.
Choose the correct graph below.
OA.
OB.
Oc.
OD.
4-
4-
4-
A
B
A
A
Transcribed Image Text:Undamped oscillators that are driven at resonance have unusual (and nonphysical) solutions. To investigate this, complete parts (a) through (e) below. (a) Find the synchronous solution Acos S2t + Bsin 2: to the generic forced oscillator equation my" + by' + ky = cos 1t. y(l) = cos C1 + V sin S2t. (b) Sketch graphs of the coefficients A and B, as functions of 2. for m = 1, b= 0.1, and k = 25. Choose the correct graph below. O A. OB. Oc. OD. 1.5 1.5 A 2.5 2.5 2.5 2.5 IB 1.5 1.5 B. (c) Now set b=0 in your formulas for A and Band resketch the graphs in part (b), with m= 1. and k= 25. What happens at 2= 5? Notice that the armplitudes of the syrchronous solutions grow without bound as 2 approaches 5. Choose the correct graph below. OA. OB. Oc. OD. 4- 4- 4- A B A A
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Free Undamped Vibrations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY