Shm And Systems Flashcards
What’s General form of shm
Acceleration. = -w2 x
So x = a sin wt + e
After doing r formula, and episokon is the PHASE SHIFT
What to always do when sketching transformations that hsve two in the brakcte?
IMPORTANT
FACTROISE the stretch out! They shift it first then stretch, so need to see
This will tel, you the correct shift
How to sketch the sun graphs easily
Find amplitude and time period by looking st omega
Points of intersections string to 0
And sketch
What do the three dampening do in word terms
Heavy dampening = when the reistsnce very large. There will be NO OSCILLATIONS , but it will take a long time for the thing to reach equilbourm
Critcal dampening = NO OSCIALLATIONS again, however this reached equilibrium in the FASTEST TIME
UNDER DAMPENING = like air resistance, there is oscialltions, and they gradually decrease in amplitude approaching 0
In each case the amplitude grsdiually approaches 0
When dampening is inolved, what EXTRA term is added into original SHM equation?
Some sort of resistance force which is acting proprtionsl to the speed of the system
Hence a k dy /dt will be added! Hence the solutions change
As with a dampening force the shm system becomes QUADRATIC, how to know exactly what type of damoenign occurs by solving the discrimination of the aixhilhary eauaiton
If more than 0, think over dampening, this leads to distinct roots but long to get to 0
If = 0, then repeated roots so the solution gets to 0 faster
If less than 0 complex roots, thid introduces sinduoial curves hence first ro acc have oscialltions in the first place that gradually decrease
Remember when talking about damped quadratic this is with a new middle term, without this it’s still normal shm
Always use AUXHILLHARY TO SOLVE EVEN IF LINEAR!
Don’t lackkk
Remmeber what 3 words to describe damping in ocr spec
Over, critical, under, based on roots! And discriminat that’s it
How to aovle system
Create a new equation by differentiating one
Now you can sub bith equations in no problem as they are separate
Sub on in, then sub the other in that will eliminate varibale
Then solve find basic for x, and basic for y . Rememebr when it is 2x habe to replace this with the solution form
Simultaneously solve and then write down don’t lack
Also stop making mistake, so,tuilsn go striagnt in not my js
Rememebr if there is a CONSTSNT in the differential system of equations how to do it
Put it to right side and use particular integral stuffs
How to show that population ends up being the same?
If same , dividing them will give you 1
As a resukt divide them, and REMOVE ONE POWER OF E by diving eveyrhtjng by it
. This is bevause you csn’t tell what one thing tends to as they have different grsifent
Now once divide it becomes eadh
