Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
If > 2√/km, the system mx" + px' + kx = 0 is over- damped. The system is allowed to come to equilibrium. Then the mass is given a sharp tap, imparting an instanta- neous downward velocity vo (a) Show that the position of the mass is given by where Vo x(t) = e-ur(2m) sinh yt. u²-4mk Y = 2m (b) Show that the mass reaches its lowest point at 2my н t= tanh1 Y a time independent of the initial conditions. (c) Show that, in the critically damped case, the time it takes the mass to reach its lowest point is given by t = 2m/u.

If > 2√/km, the system mx" + px' + kx = 0 is over- damped. The system is allowed to come to equilibrium. Then the mass is given a sharp tap, imparting an instanta- neous downward velocity vo (a) Show that the position of the mass is given by where Vo x(t) = e-ur(2m) sinh yt. u²-4mk Y = 2m (b) Show that the mass reaches its lowest point at 2my н t= tanh1 Y a time independent of the initial conditions. (c) Show that, in the critically damped case, the time it takes the mass to reach its lowest point is given by t = 2m/u.

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
4.4 21 21. If > 2√/km, the system mx" + ux' + kx = 0 is over- damped. The system is allowed to come to equilibrium. Then the mass is given a sharp tap, imparting an instanta- neous downward velocity vo (a) Show that the position of the mass is given by where Vo x(t) = e-ur/(2m) sinhạt, Y u² - 4mk Y= 2m (b) Show that the mass reaches its lowest point at t = tanh-1 2my н Y a time independent of the initial conditions. (c) Show that, in the critically damped case, the time it takes the mass to reach its lowest point is given by = 2m/u. =
Transcribed Image Text:4.4 21 21. If > 2√/km, the system mx" + ux' + kx = 0 is over- damped. The system is allowed to come to equilibrium. Then the mass is given a sharp tap, imparting an instanta- neous downward velocity vo (a) Show that the position of the mass is given by where Vo x(t) = e-ur/(2m) sinhạt, Y u² - 4mk Y= 2m (b) Show that the mass reaches its lowest point at t = tanh-1 2my н Y a time independent of the initial conditions. (c) Show that, in the critically damped case, the time it takes the mass to reach its lowest point is given by = 2m/u. =
Expert Solution
Step 1

Advanced Math homework question answer, step 1, image 1

steps

Step by step

Solved in 8 steps with 8 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