Differntiwls Equations Flashcards
When they say solve a differential under no circumstance what must you do
Leave as A!
Check start of the question some times hidden cintext starts from rest is t =0 v =0
Can you use auxiliary method if there’s some unknown varibale in front of your differentials?
NO! This is bevause you won’t be able to solve potential quadratic etc
Think I’m cintext of the question, if velocity is negative, it won’t accelerate into the ground but
rather what will happen to the rocket
The rocket will FAIL TO LEAVE THE GROUND, say that it needs positve velocity to leave!
When there is ANOTHER DIFFERENTIAL, how to remove it
Look at equation connecting them together and simply just DIFFERNIATE AND SUB IN!
Okay one model has more resistance and tends to less accelrwtion and v to other which has less resistance, how to explain this? (2)
1) just say they have less
2) consistent with having less resistance
Simple
HOW TO ALWAYS STATE THE RESISTANCE FORCE, DONT LACK
Why must include the m?
MUST take it back to newton 2nd law equation
Don’t be stupid, remember it’s gonna be mg - m something (like it said before) = ma
But the ma term MUST BE ON ITS OWN, so divide everything so it’s like that.
Now just read off the resistance force easy
Must include the m because that was ORIGINALLY PART OF THE REISSTANCE FORCE, we just divided through, don’t lack
How to tell an equation in trig is straight away SHM, and how to find the period?
IMPORTSNT
Remember if it’s in sin + cos form, this is lit called HARMONIC FORM
- so convert it it always becomes sin (xt + e) for the phase shift
But remember the only thing that affects the period is the scalar multiplier , so do 2Pi/ multiplier as normal period would be 2pi
Can you take the limit of general sin and cos graphs?
NO YOU CANT , no matter what, you know the max amplitude, but never know ar what point infinity is at
So you can’t, leave it at this
Always when q says over long time, must take some limit tho…
Remember under damp critical over damp rules?
Less than 0 = under damn , 0 = critical more than = overdamp easy
If they give a rate in an equation, obviously have ti think about the rate somehow
So they gave dx / dt, instead of trying to figure out what x is to differentiate, how about think with words
Okay x is chemical but a and b are rates, so if I link x as a rate I can to the rest,
…
How else can you link equations if you don’t know exactly what one variable is
Write down what each varibale is, x is normal but the rest were ALL RATES, so to link x to them we need the rate of x, so dx / dt
Now link this to a and b and previous q, and just re arrange
Hank about it using words if stuck next time
Remember use INFO IN QUESTIONS
If they said water was 1 litre, and now x is same quantity promotion as water what is x?
- must be a HALF, very easy 2 marks thrown do better
Fir lomg differntial equations take a second to process what’s happening in real life
So liquid being added in and removed at same time,
Now the rate of removal is TWICE the rate of adding, so when will this break down?
This will break down when no more liquid left, all has removed bevause it’s removed faster than added, and this happens after a certain time
Therefore beyond this differniate is invalid,
Use the q read it for a bit first
If it says max you will need to find DERRIVATIVE in any paper you do, even mechanics
