Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Differential Equations not solvable

  1. Mar 1, 2016 #1
    In the first image it shows the ##\alpha^2-w_0^2<0## situation whereas in the second image the situation is when ##\alpha^2-w_0^2=0##.The problem is the book says to use ##T_0=2\pi/w_0## to determine diabetes but you can't do that when ##\alpha^2-w_0^2=0## because it can't be put into a cosine function. What do I do in this situation?
     

    Attached Files:

  2. jcsd
  3. Mar 1, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I don't see the second image. Fig 2. has ##\alpha^2-\omega_0^2>0##, not = 0. But the picture doesn't look credible at all. It looks more like underdamped to me.

    Your book makes a mess of things with "three types, depending on ##\alpha^2-\omega_0^2>0##, < 0 or zero. These three types correspond to overdamped, critically damped and underdamped cases".

    Confusing, to put it mildly:
    ##\alpha^2-\omega_0^2>0 \qquad \Rightarrow ## overdamped
    ##\alpha^2-\omega_0^2=0 \qquad \Rightarrow ## critically damped
    ##\alpha^2-\omega_0^2<0 \qquad \Rightarrow ## underdamped​

    Check out a better text, e.g. here

    And yes, in the case of critical damping there are no oscillations.

    By the way, I don't hear the book saying to use ##T_0##. Did you quote correctly ?
     
  4. Mar 1, 2016 #3
    I meant Exercise 2 not the Figure 2, sorry for not pointing it out. And ##T_0## is on a different page, uploaded below.
     

    Attached Files:

  5. Mar 1, 2016 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It looks as if they want you to make quite some assumptions for this exercise: reliable measurements to begin with. G0 = 70. And no additional glucose dosing in between, ...

    If glucose concentration goes from 95 via 65 to 75 that means something significant for T0 . Agree ?

    ( Could such measurements be consistent with critical damping ? )
     
  6. Mar 1, 2016 #5
    The measurements can be consistent if the function is of the form ##(a-bt)e^{ct}## where ##a##,##b## and ##c## are positive. I don't know the actual meaning of ##T_0## but from the hint I guess it has got something to do with the level going down to normal again.
     
  7. Mar 2, 2016 #6

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    (I suppose you mean c is negative) Oh ? How do you come to that conclusion ?

    94812oct2013.png
    From http://www.uprh.edu/rbaretti/Glucose1.htm
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Differential Equations not solvable
  1. Differential equation (Replies: 3)

  2. Differential equation (Replies: 15)

Loading...