SHM Oscillstions Flashcards
Multiple choice question giving a range of frequencies a driving force drives something at and asks for light damping
What direction resonance can happen
Range of frequencies = 1 frequency will RESONATE
Whereas two diagrams showed only one frequency that didn’t resonate = this is wrong
Finally look for light damping
Remember resonance can only happen UPWARDS
Damping force and velocity? How do they compare, when is max damping force
How does damping force and accelrwtion compare direction wise?
Think about it, the damping force probably air and that depends on how fast velocity is going through it, thus it’s proprtinsl to velocity and OPPOSITE DIRECTION as it’s resistance
So at max v , centre no displacment is max driving force
2) it’s I’m the same direction half a cycle and other half it SWITCHES
What things are ALWAYS opposite each other IN SHM
Accelrwtion displacment
Velocity and damping force
Everything else (accel velocity, velocity displacement) these always switch every half turn
When there is an acceleration involved, what to say about the NORMAL of an object
This will NOT BE EQUAL TO MG , as now there is a resultant force in the DIRECTION of acceleration
Remember to only look at forces acting in body, weight and normal, only these can contribute
So it would be mg- N = ma
And rearrange
What is the least normal csn be for it to be contact
What range of values does it need to be for it to lose contact
At N = 0, it’s barely in contact
Once normal negative, it falls off
Remember what happens to the POSITION OF PEAK AMPLITUDE (resonance amplitude) UNDER HEAVY DAMPING
it occurs at a lower frequency than the normal natural frequency of the object, so it will occur SLIGHTLY LEFT
So when drawing make sure to make it slightly to the left for the MAX amplitude , the resonance one
What is difference between driving force and driving frequency
What does driving force determine
So if I increase driving frequency, do I increase amplitude linearly?
Driving force is the force that actually causes it to move
The driving force will determine/ be responsible the AMPLITUDE it has at any frequency , higher driving force higher amplitude . Driving frequency is independent
HOWEVER THE DRIVING FORCE WILL BE HAPPENING AT A CERTAIN DRIVING FREQUENCY, that can be increases across a range.
- at all frequencies it will be of same amplitude except
- AT natural frequency thr amplitude will be much higher remember due to resonance, maximum energy transfer occurs here so maximum amplitude,
(Not a case of increase driving frequency, increase driving force and thus amplitude, they’re indpeent)
Remember frequency is independent of
Amplitude
IMPORTSNT
If there is a forced oscillator, and damping at play , why is TOTAL energy of system the same and the AMPLITUDES THE SAME
So what are the amplitudes determined by (2) things
So will amplitude vary with cinstsnt drivijg firce and constsnt dampening
Thus is bevause even tho there is dampening in play, as it’s a CONSTANT DAMPENING FORCE, and energy input due ti being a constsnt Oscillating each oscislltioms is damped by the same amount each time , energy lost each time is constsnt but energy REPLENISHED IS CINSTSNT TOO
Thus it stays at the same amplitude , and total energy in system is constsnt as its always getting replenished
Thus the amplitude heights are influenced by thr DAMPENING, and also the force given by the oscislltioms
3) NO IT WILL BE CONSTANT
What is the amount if dampening influenced by based on the properties of say a weight in ball
What does dampening get influence by?
Just think if dampening as air resistance , which depends on surface area, velociy travelling, and viscosity
Thus a more heavier thing won’t cause dampening to happen more or less
In fact mass changed the tim
E period not the amplitude so don’t count thst
Same explanation ti say why dampening depend in velocity, because resistance does, so max velocity = max dampening, obv OPPSITE DIFECJTIN
How to prove something is proprtinsl and has negative ?
Must say the gradient goes through the origin thus PROPORTIONAL
As the gradient is negative , it means accelrwtion slaw has neagtive direcitin if displacment
HOW TI FIND WHEN THE MOST ENERGY DISSAPATED of oscillations constantly damping (don’t make silly mistake)
Okay the fraction of damping may be constant every half cycle, all that says is it’s expoential nice
The DAMPENING STAFTS STRAIGHT AWAY!!
Most energy lost = most dampening
Most dampening = most velocity
Most velocity = when displacment 0
However as amplitudes are changing snd v max = WA, need to pick the 0 displacment which still have the GREATEST AMPLITUDE AHEAD!! will
To say that work is done against dampeners as it moves, what to mention
It’s due ti friction or resistance that work is done against
6 MARKER ON MEASURING LENTGH AND TIME FOR LENDULUM, NEED TO GO THROUGH SLL THE TECHNIQUES WITH SIR
To find the ACCURATE time period of a graph what to do
Look at total time, and divide by TOTAL WAVES (from 0, say 3 waves, divide time by 3, gives accurate answer)
