# 0.1 Lecture 2: introduction to systems  (Page 2/8)

3/ Conclusion

A system is described structurally by specifying:

• the system topology,
• the rules of interconnection of the elements,
• functional descriptions of the elements — constitutive relations.

III. DYNAMIC ANALOGIES

Physically divergent systems can have similar dynamic properties.

1/ Mechanical free-body diagram

M = mass, B = friction constant,

K = spring constant,

f(t) = external force, and

v(t) = velocity of the mass.

Summing the forces yields

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

2/ Electric network

Summing the currents (Kirchhoff’s current law) yields

$i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}+\frac{v\left(t\right)}{R}+\frac{1}{L}{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

3/ The mechanical and electrical systems are dynamically analogous

$\begin{array}{}f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }\\ i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}+\frac{v\left(t\right)}{R}+\frac{1}{L}{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }\end{array}$

Thus, understanding one of these systems gives insights into the other.

4/ Block diagram

A block diagram using integrators, adders, and gains

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

5/ Electronic synthesis of block diagram

The integrator, adder, and gain blocks are other examples of functional descriptions of systems. We can produce a structural model of each of these blocks. For example, the gain block is easily synthesized with an op-amp circuit.

The op-amp itself is a functional model of a device that we can synthesize with an electronic circuit including a number of transistors.

Conclusion: We have seen several types of descriptions of systems

$f\left(t\right)=M\frac{\text{dv}\left(t\right)}{\text{dt}}+\text{Bv}\left(t\right)+K{\int }_{-\infty }^{t}v\left(\tau \right)\mathrm{d\tau }$

All four descriptions define a system with the same dynamic properties. We will develop methods that characterize these systems efficiently and that abstract their critical dynamic properties.

IV. CLASSIFICATION OF SYSTEMS

1/ Memoryless systems

The output of a memoryless system at some time to depends only on its input at the same time to. For example, for the resistive divider network,

${v}_{o}\left(t\right)=\frac{{R}_{2}}{{R}_{1}+{R}_{2}}{v}_{i}\left(t\right)$

Therefore, ${v}_{o}\left(\text{to}\right)$ depends upon the value of ${v}_{i}\left(\text{to}\right)$ and not on ${v}_{i}\left(t\right)$ for t ≠ to.

2/ Systems with memory

$i\left(t\right)=C\frac{\text{dv}\left(t\right)}{\text{dt}}$

$v\left(t\right)=\frac{1}{C}{\int }_{-\infty }^{t}i\left(\tau \right)\mathrm{d\tau }$

Note that v(t) depends not just on i(t) at one point in time t. Therefore, the system that relates v to i exhibits memory.

3/ Causal and noncausal systems

For a causal system the output at time to depends only on the input for t ≤ to, i.e., the system cannot anticipate the input.

Physical systems with time as the independent variable are causal systems. There are examples of systems that are not causal.

• Physical systems for which time is not the independent variable, e.g., the independent variable is space (x, y, z) as in an optical system.
• Processing of signals where time is the independent variable but the signal has been recorded or generated in a computer. Processing is not in real time.

4/ Stable and unstable systems

Stability can be defined in a variety of ways.

Definition 1: a stable system is one for which an incremental input leads to an incremental output.

An incremental force leads to only an

incremental displacement in the stable

system but not in the unstable system.

Definition 2: A system is BIBO stable if every bounded input leads to a bounded output. We will use this definition.

#### Questions & Answers

guys I need to know what is meant by basic economic mathematics and explain please
It's also the usage of mathematical tools to express and analyse economic problems.
Rasaq
so basically it's the use of mathematical formulas to solve the problems under demand and supply right...
Lovemore
Yes, though economic analysis majorly has to deal with demand and supply forces in fact the back bone of economics rest on demand and supply but there are other functions like consumption function, implicit ,explicit, monotonic( constant, increasing, decreasing), transcendential, homogeneous, polyn
Rasaq
wat improvement do economic has with our life
it help us how to use our limited resources to satisfy our unlimited wants
Pagnol
Economics assit in understanding the pre-requisite for Growth and developmen and how the workings of the economy operates.
Rasaq
Economics is the social Science in which we study how scarce resources are allocated for the betterment of human being.
what is equilibrium point
where price and quantity demanded meet
Pagnol
is the point where price an quantity demanded meet
Aminata
why do consumer demand curve tend to move downward slope
Aminata
Equilibrium point is the point at which quantity demand equals quantity supply.
Rasaq
What is monopoly
Is a strict example of an imperfect market where there is only one seller and many buyer for a particular product.
Rasaq
what is economics
economics us behavior. Of people, nations, markets etc. It has much to do with reactions. watch MSNBC. Bloomberg. everyday they talk about how the markets react to an piece of news, legislation, interest rates etc. Interesting volatile stuff
TOM
but, it also react with science
ezhilarasan
economic is a science with study's the behavior of people,market and price
Bertilla
it's a science which study the behavior of people ,market n price
Bertilla
What is opportunity cost?
Junior
opp. cost~a benefit, profit or value of something that must be given up to acquire or achieve something else
Kim
or something that you foregone
Kim
who is the father of economic
shaikh
modern father is Adam smith
Bilal
Nazifi
what is backward bend
It's a curve that reverses direction
Good evening friends
Kojo
Evening
evening
Emmanuel
hi
Lawrence
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Suleiman
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Kojo
hello
James
yeah
Kojo
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Kojo
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James
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Kojo
Ok
James
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Junior
morning all
Emeka
Morning
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Maaz
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Marwa
marwa no
Maaz
how economic effect the Market
Abdikarem
what is the difference between statistic and statistics?
Shafiu
One of the Principle of Economics states "Market is the best place to organize economic activies". However, market may fail if it does not perform it's necessary expected functions like Exercising real forces of demand and supply, contact where transactions are made etc. Though government may int
Rasaq
Through the Business cycle or the trade cycle.
Rasaq
it can can be described as when the demand is insufficient
high Dublin divino through Higginbotham
How does exchange rate affect the demand and supply?
austine
You mean demand and supply of currency ?
Jahangir
Hello
Hann
Hi
Jahangir
Am debby
Hann
am jahangir
Jahangir
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Ogunsola
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Jahangir
doing great
Ogunsola
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Mudassar
Am gud
Hann
Gd
Mudassar
Ogunsola
are you help for your country of economy leavel
Mutha
hi
Hammed
Hello
Assan
hi
Pranshi
Hello
Kamal
hi
Pranshi
hi
Abbas
hi
Abdirazak
ki sah botine
Neyshawn
hi
Nasir
Hello Economist
Nasir
hello
Victor
Hie... may anyone give me examples of countries that successfully implemented import substitution industrialisation.
Thabo
Nigeria
Junior
hey I'm emma from Uganda
niwagaba
Hello
Abraham
What is the difference between Demand and Quantity Demanded?
Weedh
Demand refers to how much a product is desired by buyer mean while quantity demanded refers to the amount of product a buyer is willing to buy at a certain price.
Junior
Good evening
Evening
Junior
evening
Ogunsola
someone wat is d textbook to read for banking and finance course
ayomide
Evening
Anjorin
Hw r u doing
Faku
yh
Benj
I'm good, u?
Anjorin
demand is the various quantity of goods or services a consumer is Willing and able to buy at a particular price over s given period of time while quantity demanded is the amount of goods or services being paid for
Florence
Good
Awudu
1.it allows producers to learn and invent 2.it allows agent to take advantage of economic scale 3.it allow agents to focus in areas of
can someone explain the motive of money to me?
ask the question you don't know
ojo
opportunity cost
Sylvo
the motive of money is to pay for goods or services. it's also for transaction purposes bet it ordinary or unforseen
Silke
Money helps to reduce our scarcity problems. It can satisfy your wants to an extent
Okwori
transactive motive
Aminata
money help as a store of value for future uses
Pagnol
it also serve as a medium of exchange
Pagnol
The motive of Money was postulated by John Maynard Keynes when he was explaining the Theory of Money from the Keynesian point of view. These motives are; the speculative motive, the transaction motive and the Precautionary motive. The precautionary motive of money is an assumption that mone
Rasaq
How dose economics use science methods to explains it problems
according to Jhon Robinson the main problem of economics is what to produce? how to produce? whom to produce? economics tries to solve these problem scientifically by using its theories which are scientific in nature,basically micro and macro theories which just explain what the problem is...
Lavkesh
and now the solving techinique is also changed. only theories or its matematical +statistical version is not sufficient so the economist had developed Econometrics which includes economic theory+mathematical economics+statistics, for solving economic problem. This method treats economics as a pure
Lavkesh
..pure science so this technique is based on pure scientific methods.
Lavkesh
Economics is the scientific study of human behavior so there for science is used to solve economics problems using economics theories
Florence
economic is not higly subject of taminadu ...
Mutha
Through observations, formulation of hypothesis and derivation of a conclusion.
Rasaq
so what can you say about basic economic mathematics and explain please......
Lovemore
It's an approach in which Economist make use of mathematical symbols or mathematical parameters to express an assertion or theory.
Rasaq
measurement of elasticity of demand
Price elasticity of demand= Percentage change in quantity demanded/ Percentage change in price
Jale
For example, suppose that a 10 percent increase in the price of an ice-cream cone causes the amount of ice cream you buy to fall by 20 percent. We calculate your elasticity of demand as
Jale
Price elasticity of demand =20 percent /10 percent = 2
Jale
In this example, the elasticity is 2, reflecting that the change in the quantity demanded is proportionately twice as large as the change in the price.
Jale
what is economic
economics is a social science that studies the relationship of human behavior between ends and scare...
Lawrence
Why is economics as a subject is so important to human being?
austine
it's significant in study of managing available resources to satisfy human needs and wants
mohamed
economics is the science of wealth
Aamir
it is also said that it is the science of scarcity
Aamir
why study economic
Neo
Economic helps to meet our needs and wants nd to make choices.
Abraham
careers or jobs associated with economics
Neo
Economics is more than choices, scarcity, resources etc. It has a lot to do with psychology, social psychology. Understand motivation for consumer decisons.
TOM
okey
Neo
I what to study economic understand education what subject will I take in my jamb
DIRIOHA
English.mathematics.economics and one other social science subject
Ogunsola
economic is life start to end
Mutha
Plz help in lectures job for economics
Mudassar
acc to robbin . "Economics is a science that studies human behaviour as a relationship between scarce means and ends which have alternative uses"
Jahangir
Economics is important to man "human wants are insatiable
Hann
pleas explain circular flow of income
Eagle
what is economic growth
Samuel
Economic growth is an increase in the real output leading to a growth or a rise in the nations gdp.
Charles
Economics is the study of wealth or money and it's an economic activity which has almost three terms divided into them, production consumption and Distribution of wealth.
Zahid
Economics is the study of wealth or money and it's an economic activity which has almost three terms divided into them, production consumption and Distribution of goods and services.
Zahid
plz what is econometrix
saheed
Econometrics is the Mathematical/Statistical Representation of economic systems we analyze theoretically and empirically
Jason
Econometrics is the statistical application to the empirical estimation of economic relationship
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