anonymous
  • anonymous
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(4-1.9^2)/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))
MIT 18.03SC Differential Equations
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.