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
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
Related questions
Question
Sub-
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0464e5f-558f-4b62-8e27-7aacf8c7bfc8%2F9b3fd6f3-3df6-42cd-a04b-753e5e0b5338%2Fs3oo75c_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0464e5f-558f-4b62-8e27-7aacf8c7bfc8%2F9b3fd6f3-3df6-42cd-a04b-753e5e0b5338%2Fb3mve0s_processed.png&w=3840&q=75)
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
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