Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
pjcappaert
Group Title
Why is it said that critical damping leads to the fastest decay? If a system with amplitude 1 is slightly underdamped it crosses the x axis but it's absolute value is less than that of the system with critical damping up to f(x) ~ 10^25.
For the system: x''+cx'+x=0
critical damping (c=2)
x=e^(x)+x*e^(x)
underdamped (c=1.9, wd=sqrt(41.9^2)/2)
x=e^(x*b/2)*cos(wd*x)+(b/2/wd)*sin(wd*x)
=e^(x*1.9/2)*(cos(.39^.5/2*x)+(1.9/.39^.5)*sin(.39^.5/2*x))
 one year ago
 one year ago
pjcappaert Group Title
Why is it said that critical damping leads to the fastest decay? If a system with amplitude 1 is slightly underdamped it crosses the x axis but it's absolute value is less than that of the system with critical damping up to f(x) ~ 10^25. For the system: x''+cx'+x=0 critical damping (c=2) x=e^(x)+x*e^(x) underdamped (c=1.9, wd=sqrt(41.9^2)/2) x=e^(x*b/2)*cos(wd*x)+(b/2/wd)*sin(wd*x) =e^(x*1.9/2)*(cos(.39^.5/2*x)+(1.9/.39^.5)*sin(.39^.5/2*x))
 one year ago
 one year ago

This Question is Closed

pjcappaert Group TitleBest ResponseYou've already chosen the best response.0
I looked in a textbook and saw that the wording in the 18.03 lecture notes is not ideal. In the textbook the wording was "fastest decay without oscillation." I agree with this statement.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.