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Bounding curves in harmonic motion
Harmonic motion graphs may be enclosed by bounding curves. When a function has a varying
amplitude , such that the amplitude rises and falls multiple times within a period, we can determine the bounding curves from part of the function.
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Key equations
Standard form of sinusoidal equation |
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Simple harmonic motion |
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Damped harmonic motion |
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Key concepts
- Sinusoidal functions are represented by the sine and cosine graphs. In standard form, we can find the amplitude, period, and horizontal and vertical shifts. See
[link] and
[link] .
- Use key points to graph a sinusoidal function. The five key points include the minimum and maximum values and the midline values. See
[link] .
- Periodic functions can model events that reoccur in set cycles, like the phases of the moon, the hands on a clock, and the seasons in a year. See
[link] ,
[link] ,
[link] and
[link] .
- Harmonic motion functions are modeled from given data. Similar to periodic motion applications, harmonic motion requires a restoring force. Examples include gravitational force and spring motion activated by weight. See
[link] .
- Damped harmonic motion is a form of periodic behavior affected by a damping factor. Energy dissipating factors, like friction, cause the displacement of the object to shrink. See
[link] ,
[link] ,
[link] ,
[link] , and
[link] .
- Bounding curves delineate the graph of harmonic motion with variable maximum and minimum values. See
[link] .
Section exercises
Verbal
Explain what types of physical phenomena are best modeled by sinusoidal functions. What are the characteristics necessary?
Physical behavior should be periodic, or cyclical.
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What information is necessary to construct a trigonometric model of daily temperature? Give examples of two different sets of information that would enable modeling with an equation.
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If we want to model cumulative rainfall over the course of a year, would a sinusoidal function be a good model? Why or why not?
Since cumulative rainfall is always increasing, a sinusoidal function would not be ideal here.
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Algebraic
For the following exercises, find a possible formula for the trigonometric function represented by the given table of values.
Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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