Homework Help is Here – Start Your Trial Now!
Science
Physics
Q3: The time dependance of the position x(t) of an underdamped oscillator (of drag co- efficient c and spring constant k) can be described by a sinusoidal curve with exponentially decaying amplitude. So, one can conventionally plot exponential-decay functions f(t) and -f(t) that "sandwich" æ(t) and mimic its exponential decay. Both f(t) and its mirror image -f(t) touch r(t) at some time instances t, and t,, respectively, where n = 1, 2, 3, - ... (See Fig. 3.4.3 in your assigned textbook). Following the same convention of the constants y and wa as we did in the class, suppose that x(t) is given by æ(t) = Aet cos(wat), and, hence, f(t) is given by f(t) = Ae-", then solve the following (a) Find the first two instants of time to and t, at which f(t) and – f(t) touch x(t). (b) Since r(t) is oscillatory, it has multiple local maxima. Suppose that {Tn} are the time instances at which æ(t) has a local maximum, where n = 1, 2, 3, -.. , then find 71 and T2. (c) Discuss the results you obtained from the previous two parts. (d) Comapre the ratio al and Cl and comment about the results. r(Tn+1). 1(Tn) r(t,)

Q3: The time dependance of the position x(t) of an underdamped oscillator (of drag co- efficient c and spring constant k) can be described by a sinusoidal curve with exponentially decaying amplitude. So, one can conventionally plot exponential-decay functions f(t) and -f(t) that "sandwich" æ(t) and mimic its exponential decay. Both f(t) and its mirror image -f(t) touch r(t) at some time instances t, and t,, respectively, where n = 1, 2, 3, - ... (See Fig. 3.4.3 in your assigned textbook). Following the same convention of the constants y and wa as we did in the class, suppose that x(t) is given by æ(t) = Aet cos(wat), and, hence, f(t) is given by f(t) = Ae-", then solve the following (a) Find the first two instants of time to and t, at which f(t) and – f(t) touch x(t). (b) Since r(t) is oscillatory, it has multiple local maxima. Suppose that {Tn} are the time instances at which æ(t) has a local maximum, where n = 1, 2, 3, -.. , then find 71 and T2. (c) Discuss the results you obtained from the previous two parts. (d) Comapre the ratio al and Cl and comment about the results. r(Tn+1). 1(Tn) r(t,)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question

question c and d please

Q3: The time dependance of the position 2(t) of an underdamped oscillator (of drag co- efficient c and spring constant k) can be described by a sinusoidal curve with exponentially decaying amplitude. So, one can conventionally plot exponential-decay functions f(t) and -f(t) that "sandwich" x(t) and mimic its exponential decay. Both f(t) and its mirror image -f(t) touch r(t) at some time instances t„, and t,, respectively, where n = 1,2, 3, -... (See Fig. 3.4.3 in your assigned textbook). Following the same convention of the constants y and wa as we did in the class, suppose that #(t) is given by x(t) = Ae cos(wat), and, hence, f(t) is given by f(t) = Ae-. then solve the following (a) Find the first two instants of time to and t, at which f(t) and - f(t) touch x(t). (b) Since r(t) is oscillatory, it has multiple local maxima. Suppose that {Tn} are the time instances at which x(t) has a local maximum, where n = 1, 2, 3, -.., then find T1 and T2. (c) Discuss the results you obtained from the previous two parts. (d) Comapre the ratio tatl and (nt1l and comment about the results. I(tn) I(Tn) Q4: (Optional) Investigate the motion of a harmonic oscillator subject to a damping force of constant magnitude.
Transcribed Image Text:Q3: The time dependance of the position 2(t) of an underdamped oscillator (of drag co- efficient c and spring constant k) can be described by a sinusoidal curve with exponentially decaying amplitude. So, one can conventionally plot exponential-decay functions f(t) and -f(t) that "sandwich" x(t) and mimic its exponential decay. Both f(t) and its mirror image -f(t) touch r(t) at some time instances t„, and t,, respectively, where n = 1,2, 3, -... (See Fig. 3.4.3 in your assigned textbook). Following the same convention of the constants y and wa as we did in the class, suppose that #(t) is given by x(t) = Ae cos(wat), and, hence, f(t) is given by f(t) = Ae-. then solve the following (a) Find the first two instants of time to and t, at which f(t) and - f(t) touch x(t). (b) Since r(t) is oscillatory, it has multiple local maxima. Suppose that {Tn} are the time instances at which x(t) has a local maximum, where n = 1, 2, 3, -.., then find T1 and T2. (c) Discuss the results you obtained from the previous two parts. (d) Comapre the ratio tatl and (nt1l and comment about the results. I(tn) I(Tn) Q4: (Optional) Investigate the motion of a harmonic oscillator subject to a damping force of constant magnitude.
Expert Solution
steps

Step by step

Solved in 4 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS