Question 30 (this year's HSC Mathematics Advanced exam)

[Uniquecapture]

Eddie, you were born to be a maths teacher. I really hope your students realise how lucky they are to have you.

[lyingcat]

In Aviation an aircraft’s stability characteristics can be represented by a graph with this shape. The Cessna 172 has this desirable characteristic:) where X is the airplane’s pitch attitude and Y being time.
If trimmed for level flight and you pull back abruptly on the yoke and let go, the plane will pitch back down negative and back positive for a short time, it will oscillate but quickly stabilize back to level flight. This is called a Positive Dynamic Stability.
The opposite of this graph is called a Negative Dynamic Stability and a plane with this characteristic we’re in level flight and you let go of the pitch control, even a small amount of turbulence will cause the plane to oscillate, pitching up and down more and more until eventually the wing would stall.
I believe fighter jets are dynamically unstable due to the design trade off making it wayyy more maneuverable. But this would require constant control adjustments to maintain a stable pitch attitude… or roll and yaw for that matter. This is way the flight computer adjusts the control surfaces to maintain stability. The pilot’s controls actually tells the computer what they want the plane to do and the computer makes it happen.

[theflash]

not the age demographic at all for this (22years old) but love his videos. amazing communication and teaching. it's fun watching easy concepts get explained by a pro. cheers!

[matmagix]

Back in the day, I remember plotting these types of functions (products and quotients, composition of various elementary functions) in Extension II and my teacher had an approach that did not typically involve calculus because the graph could technically be resolved "by inspection" and a choice table of function values ("anything times 1 is itself", "anything times -1 is negative itself", "anything times 0 is 0", dividing by a very large number tends to 0, and dividing by a very small number tends to infinity")

[Quarker]

Did extension maths more than a decade ago and barely any of this makes sense anymore 😢 Eddie is a legend tho and every student deserves a teacher with his passion and enthusiasm for education

[Radictor]

I knew very little of this but I still managed to guess/prempt somethings just because of the clear explanation.

[TheFinalMinutes]

What was the question again please sir? My brain melted about 45 seconds in. I just don't get equations and never will - my brain doesn't work that way. Good on those of you who can understand this! (I'm jealous in the nicest possible way).

[KevinAPamwar]

Nice....

Maxima & Minima of a function

F'(x) =0 for Maxima & Minima

U can also plot for F(x) for x = pi/2 and x = 3*pi/2

[markkennedy]

I'm gonna finish me HSC this avo, then go to uni. Fair dinkum.

[melbournegt]

This is a damped harmonic response found in control system engineering

[MathsMadeSimple]

Knock knock. Who's there?

Mr. Mr woo?

[ShiojSharma]

Sir please try JEE Advanced mathematics problems.

[michaelgallagher]

0 1 2 3 4 5 6 7 8 9 10 11 12 / 13 14 15 16 17 18 19

[RexxSchneider]

I worry about a maths lecturer who thinks that a damped oscillation is a "weird shape". Maybe he needs to get out into the real world where damped oscillations are commonplace?