How to determine if my equation is equal to, less that or more then 0?

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James Perkins
James Perkins 2019-10-14
评论： J Chen 2019-10-14
Hi,
Im trying to solve 2nd order ODE's and determine if the solution is critically damped, over damped or under damped.
I rearranged the formula and inputted the equation to solve the quadratic equation (which works) however i cannot get the IF statement to tell me when if D=0, D<0 or D>0. Is this running into problems with the complex numbers?
Please could someone point me in the correct direction with the IF statements?
A section of the script can be seen below:
a = 1
b = 1
c = 1
D = sqrt((b^2/(4*a^2))-(c/a));
if D>0
disp('Over Damped')
elseif D<0
disp('Under Damped')
else D==0
disp('Critically Damped')
end
  2 个评论
Jos (10584)
Jos (10584) 2019-10-14
Did you debug your code, by for instance, displaying D before the if statement (remove the semicolon)?
James Perkins
James Perkins 2019-10-14
Yes, this makes no difference.
In my command window i get the below
S2 =
-0.5000 - 0.8660i
D =
0.0000 + 0.8660i
ans =
logical
0
Index exceeds the number of array elements (11).

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采纳的回答

J Chen
J Chen 2019-10-14
  1. The result of sqrt((b^2/(4*a^2))-(c/a)) is a complex number. You can't compare it with 0 (a real number)
  2. The formula for damping ratio is probably wrong. Should it be b/(2*sqrt(a*c)?
  2 个评论
James Perkins
James Perkins 2019-10-14
  1. The result of sqrt((b^2/(4*a^2))-(c/a)) is a complex number. You can't compare it with 0 (a real number)
  2. The formula for damping ratio is probably wrong. Should it be b/(2*sqrt(a*c)?
Reply:
  1. Thank you for pointing this out, i have removed the 'sqrt' so that i just have a negative number which i should be able to relate to 0.
  2. I was told that there are different ways of determining the damping style? i have adjusted this to (b^2)-(4*a*c) which is what my lecturor has advised.
Im still getting an error saying "Index exceeds the number of array elements (11).". Can someone explain what this could be?
J Chen
J Chen 2019-10-14
The damping ratio is defined as r = b/(2*sqrt(a*c)) = b^2/(4*a*c). It is under damped if r<1 and critically damped if r=1, etc. Your error came from other programming error. It's not related to the formula.

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