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

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James Perkins 2019-10-14

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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

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Jos (10584) 2019-10-14

Did you debug your code, by for instance, displaying D before the if statement (remove the semicolon)?

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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Answer 1

J Chen 2019-10-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/485214-how-to-determine-if-my-equation-is-equal-to-less-that-or-more-then-0#answer_396279

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)
The formula for damping ratio is probably wrong. Should it be b/(2*sqrt(a*c)?

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James Perkins 2019-10-14

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)
The formula for damping ratio is probably wrong. Should it be b/(2*sqrt(a*c)?

Reply:

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.
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 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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