Phy 206 Test 2

Front 1

TRUE OR FALSE:

The modern origin of nonlinear dynamics can be linked to the study of geckos and mealworms.

Back 1

FALSE

Front 2

TRUE OR FALSE

The path of sheet falling in the air is random.

Back 2

FALSE

Front 3

TRUE OR FALSE

Period 16 motion was clearly visible in the lab when we looked at the bouncing stell ball.

Back 3

FALSE

Front 4

TRUE OR FALSE

A Phase Space can include all any measurable quantity.

Back 4

TRUE

Front 5

TRUE OR FALSE

A period three orbit can double into a period 6 orbit as the relevant control parameter is changed.

Back 5

TRUE

Front 6

TRUE OR FALSE

All objects falling through the air are accurately described by linear physics.

Back 6

FALSE

Front 7

TRUE OR FALSE

Period 7 motion cannot happen in a periodic system.

Back 7

FALSE

Front 8

Non-linear dynamics is a field of study with _______.

Back 8

APPLICATIONS TO MANY DISCIPLINES.

Front 9

A pendulum is moving with its greatest velocity toward the point of maximum postive position when it is at point...

Back 9

D, THE TOP POINT

Front 10

At what point is the pendulum at its greatest deflection point?

Back 10

POINT B, POINT ON THE RIGHT SIDE

Front 11

Linear approximations are pretty good at describing the motion of _____.

Back 11

A HOCKEY PUCK SLIDING AT A CONSTANT SPEED ON ICE

Front 12

Nonlinear descriptions are required to describe the motions of ______ falling in air currents near the earth's surface.

Back 12

SMALL DUST PARTICLES

Front 13

The period 4 region of the bifurcation map is approximately ____ the period 8 region for the corresponding paramete.

Back 13

FOUR- FIVE TIMES THE SIZE OF

Front 14

The study of physics is based on the simple concept that we wish to describe _____.

Back 14

THE WORLD AROUND US

Front 15

To describe the world around us, in many situations this comes down to describing the ____ of an object and its its interactions with other objects with simple ______ statements.

Back 15

MOTION, PREDICTIVE

Front 16

When describing the motion of a ball of mass, the equation is derived from Newton's second law. It is valid until until the ball _____ _____, so long as there is no ____ ____ and the acceleration is _____.

Back 16

HITS SOMETHING

AIR RESISTANCE

CONSTANT

Front 17

We see that a ball's position and velocity depend nonlinearly on its own ______.

One of the main consequences of of this nonlinearlity is that the ball will reach a ____ ____, called the terminal velocity, if it falls for a long enough time.

Back 17

VELOCITY

MAXIMUM VELOCITY

Front 18

____ is very common in everyday experiences, even when it is small enough or if it operates over a short interval of time.

Back 18

DRAG

EX. EASIER TO RUN WITH A 10 MI/HOUR WIND, NOT INTO IT

OUTFIELDER CAN TELL WHERE BALL WILL LAND ONCE IT HAS BEEN HIT, WORRIES ABOUT ACCELERATION DUT TO GRAVITY

PEDESTRIAN CAN TELL WHEN ITS SAFE TO CROSS THE ROAD, CAN PREDICT WHERE THE CAR WILL BE, IF IT WILL STOP OR KEEP GOING

Front 19

When do nonlinear affects become important?

Back 19

NO SHORT ANSWER, MUST BE SUSPICIOUS WHEN SOMETHING UNEXPECTED HAPPENS

RABBIT IS CAPABLE OF PREDICTING THE PATH OF A FOX CHASING IT, SO IT CHANGES ITS OWN PATH AS NEEDED

Front 20

In general, predators and prey are very good at predicting future locations of_ _____ _____.

Back 20

MOVING OBJECTS

Front 21

How does nonlinearity affect birds and pilots?

Back 21

A BIRD ON A WINDY DAY

IF THE WIND IS STEADY, THE BIRD WILL HAVE NO TROUBLE WHEN APPROACHING ITS LANDING, IT WILL EVEN TURN SLIGHTLY CROSSWAYS TO THE WIND

PIKOTS ALSO DO THIS BECAUSE IT IS THE BEST WAY TO KEEP ON THE CORRECT PATH OF FLIGHT

Front 22

Why do birds have trouble landing on a branch if the wind is gusty?

Back 22

BECAUSE THE WIND VAIRES IN A NONLINEAR MANNER, THE EXACT MOTION OF THE BIRD AND THE BRANCH MAY VARY IN A COMPLICATED WAY THAT THE BIRD CANNOT FOLLOW

Front 23

Linear motions are easy, but motions resulting from nonlinear forces can become _____________.

Back 23

COMPLICATED QUICKY

Front 24

In the 17th century, motion with a nonlinear time dependence could be described for a limited time period, even the result of drag could be predicted.

But, these descriptions are limited in ____ and for _____ systems.

Back 24

TIME, SIMPLE

Front 25

As scientists gained experience with the simplest of systems, they were able to approach more ________ problems. Physicits moved from studying mechanics as an _________ field to including _________ phenomenon.

Back 25

COMPLICATED

ISOLATED

ELECTROMAGNETIC

Front 26

By the end of the 19th century, linear equations dominated the physicit's description of the _____, any nonlinear dependence was ignored or treated as a ___________.

Back 26

UNIVERSE

SPECIAL CASE

Front 27

Two sceintific revolutions occured simaltaneously in the first half of the 20th century, _____ and _____ ________.

Back 27

RELATIVITY

QUANTAM MECHANICS

TAKEN TOGETHER, THESE THEORIES ALLOWED SCIENTISTS TO STUDY THE VERY BIG, VERY SMALL AND VERY FAST.

LIMITED FOR THE MOST PART TO LINEAR PHENOMENON.

Front 28

With the advent of ______ _________, our understanding of the very small led to the construction of the first transistor and the tremendous leaps in computer technology in the 50s.

Back 28

QUANTAM MECHANICS

Front 29

With the use of computers, _______ processes could be effectively modeled.

Back 29

NONLINEAR

Front 30

Not only do nonlinear processes happen in both the ______ and _______ areas of physics, but in areas outside of physics.

Back 30

CLASSICAL, QUANTAM

AREAS INCLUDE ECONOMICS, SOCIOLOGY AND BIOLOGY

Front 31

Physicists broadened their area of interest and expertise to include the study of any _____ system: any system that evolves in ___ according to some well defined set of rules.

Back 31

DYNAMICAL
TIME

Front 32

______ ________ might be the person most assoiciated with the creation of modern nonlinear dynamics. He developed a computer model of _________. It didn't work that well, but it showed some very complex behaviors.

Back 32

EDWARD LORENZ, WEATHER

Front 33

James Yorke ran across Lorenz's work and realized the significance of the complicated _________ patterns, but it wasn't only limited to that. The complicated patterns also existed in ______.

Back 33

WEATHER, NATURE

Front 34

A simple example from ________ biology is so well suited to introduce many of the concepts central to _______ dynamics that it has become the prototype equation.

Back 34

POPULATION, NONLINEAR

THIS EQUATION, THE LOGISTIC EQUATION IS FIRST USED TO DESCRIBE THE CHANGE OF POPULATION OVER TIME

Front 35

_____ are used quite often in nonlinear dynamics because they allow us to represent some set of information about a system in a 2 or 3 dimensional form.

Back 35

MAPS

Front 36

To understand how to make a map of a system that varies in time, consider the motion of a simple pednulum (a ball of mass tied to a very light string). If you pull back on the ball and let it go, the ball will oscilate back and forth about the _______ position.

Back 36

EQUILIBRIUM

IN PARTICULAR, THE MASS WILL INCREASE VELOCITY UNTIL IT REACHES THE EQUILIBRIUM POISTION AND THEN THE VELOCITY DECREASES UNTIL IT REACHES ITS PEAK AMPLITUDE.

Front 37

A ______ ______ is just really a map with as many dimensions as is necessary to show all of the important features that represent the motion of an object or system.

Back 37

PHASE SPACE PLOT

Front 38

Phase space plots are NOT limited to _____ and ____.

Back 38

POSITION AND VELOCITY

CAN BE CONSTUCTED FROM POSITION AND MOMENTUM IF ITS MORE CONVENIENT

Front 39

In a phase space plot, initally the position is at its maximum _____ value and its velocity is ___. As time increases, the pendulums trajectory follows a ______ path in the ________ direction.

Back 39

POSITIVE
ZERO
CIRCULAR
CLOCKWISE

Front 40

The trajectory of a pendulum in position is the _______ _____ ________

Back 40

VELOCITY PHASE SPACE

Front 41

As with the pendulum, a description of a ball of mass will likely include the ____ and _____ (or speed and direction) of the ball.

Back 41

VELOCITY, POSITION

Front 42

Since you know the mass and velocity of the ball, the __________ energy and _____ are redundant.

Back 42

KINECTIC, MOMENTUM

SAME CAN BE SAID POTENTIAL ENERGY SINCE YOU KNOW THE BALL'S POSITION

Front 43

For a simple case of a ball dropped onto a table from some initital height above the table, you could make a plot of its positions as a function of ______.

Back 43

TIME

Front 44

BOUNCING BALL

Since the table is not moving, the ball bounces, but with each bounce it looses soem _______ and does not bounce as _________.

Back 44

ENERGY, HIGH

Front 45

We define positive velocity as whent he ball is moving ________.

Back 45

UPWARD

Front 46

We define positive position when the ball is above the ________ _________ of the table.

Back 46

CENTER POSITION

Front 47

Once the velocity becomes positive, the ball begis to move _______ and will reach its most _______ valie.

Back 47

UPWARD, POSITIVE

Front 48

The deacying motion of the ball is apparent when the ball looses energy with each _____ and ends up _____ on the stationary table.

Back 48

IMPACT, STATIONARY

Front 49

_______ is the term applied to a system that appears to be disordered, but has an underlying order.

Back 49

CHAOS

Front 50

The complete lack of correlation between con flips yeilds the _____ sequence of head and tails. No correlation between the results of current or any future coin flip.

Back 50

RANDOM

Front 51

Once a system parameter has been increased until the system becomes _______, a further increase in the paramter may return the system to _____ behavior.

Back 51

CHAOTIC, PERIODIC

Front 52

Observation of a period ____ window is clear evidence that the system wil exhbiti ________ behavior with an appropriate choice of parameters.

Back 52

3, CHAOTIC

Front 53

As the table frequency increases, the peak height of the ball continues to bifurcate until it becoms _______.

Back 53

CHAOTIC

Front 54

After the onset of choas, there are windows of _______ behavior and even a period 3 window.

Back 54

PERIODIC

Front 55

The major feautures of the bifurcation diargram for the bouncing ball are very similar to the features of the ______ equation.

Back 55

LOGISTIC

Front 56

The bouncing ball system is a more complex (higer dimensional) system than the _________ equation.

Back 56

LOGISTIC

Front 57

For any system, the return map can be used to predict ______.

Back 57

WHERE THE SYSTEM WILL BE AT A FUTURE TIME

Front 58

The time evolution of a _______ can be determined from the examination of the return map.

Back 58

TRAJECTORY

Front 59

The Feigenbaum equation was named thing because he was the first to recognize that corresponding ratios for __________ arising in many low dimensionl systems cover of the universal value of 4.669.

Back 59

PERIOD DOUBLING SEQUENCE

Front 60

Feigenbaum showed this was exactly true for systems with __________ in which there was only one Xn+1value for each Xn. This is called _________.

Back 60

RETURN MAPS, UNIMODAL

Front 61

We can see that points that are initially in very close _______ on the return map can have very _________ trajectories after just a few iterations.

Back 61

PROXIMITIES, DIFFERENT

Front 62

If we make a plot of return maps for two trajectories, we find the points fall ont he same curve. This is called...

Back 62

SENSITIVTY TO INITIAL CONDITIONS

THIS CAN BE SEEN IN ANY CHAOTIC SYSTEMS