# 10.2 Simple harmonic motion: a special periodic motion  (Page 4/7)

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## Conceptual questions

What conditions must be met to produce simple harmonic motion?

(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion?

(b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.

As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly. Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer.

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

## Problems&Exercises

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?

$2\text{.}\text{37}\phantom{\rule{0.25em}{0ex}}\text{N/m}$

If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same?

A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?

0.389 kg

By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?

Suppose you attach the object with mass $m$ to a vertical spring originally at rest, and let it bounce up and down. You release the object from rest at the spring’s original rest length. (a) Show that the spring exerts an upward force of $2.00\phantom{\rule{0.25em}{0ex}}\mathrm{mg}$ on the object at its lowest point. (b) If the spring has a force constant of $\text{10}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{N/m}$ and a 0.25-kg-mass object is set in motion as described, find the amplitude of the oscillations. (c) Find the maximum velocity.

A diver on a diving board is undergoing simple harmonic motion. Her mass is 55.0 kg and the period of her motion is 0.800 s. The next diver is a male whose period of simple harmonic oscillation is 1.05 s. What is his mass if the mass of the board is negligible?

94.7 kg

Suppose a diving board with no one on it bounces up and down in a simple harmonic motion with a frequency of 4.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 75.0-kg diver on the board?

The device pictured in [link] entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring constant.

(a) If the spring stretches 0.250 m while supporting an 8.0-kg child, what is its spring constant?

(b) What is the time for one complete bounce of this child? (c) What is the child’s maximum velocity if the amplitude of her bounce is 0.200 m?

A 90.0-kg skydiver hanging from a parachute bounces up and down with a period of 1.50 s. What is the new period of oscillation when a second skydiver, whose mass is 60.0 kg, hangs from the legs of the first, as seen in [link] .

1.94 s

#### Questions & Answers

what are the factors that affect international organization
Organizational structure,communication,mission
Ogunsola
what is international organization
discuss how international organization affect business in Nigeria
Imeobong
An international organization is an organization with an international membership, scope, or presence.
Avishek
thanks
Imeobong
what are the factors that affect demand and commodity
if a firm stays on the same isoquant it means ? a. output missteps decrease b. output must stay. the same c. output must increase d. quantity of labour and capital employed must remain the same e. none
A
Were
A
alyssa
B
SEMAN
A
Darren
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Bertilla
D
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Foley
d
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Alicia
a
Mohammed
hi
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d
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d) none. because isoquants meant different combination of inputs give same level of out and higher the isoquants gives higher the level of output
ezhilarasan
okay
Bertilla
analyse this table showing how this affect the law of diminishing demand return
What are diminishing marginal returns as they relate to costs?
michael
what are diminishing demand
Bertilla
please can you explain it to me because am new to economics
michael
the law of diminishing state that as more and more variable factor is added to a fixed cost, it will increase first and later its begins to fall until its get to zero. that were ur mc equal to zero
Fasae
thanks dr
Bertilla
The law of diminishing demand states that, if the price of a product is raised, a smaller quantity will be demanded and if the price of a product is lowered, a greater quantity will be demanded.
Were
The law of diminishing returns, also referred to as the law of diminishing marginal returns, states that in a production process, as one input variable is increased, there will be a point at which the marginal per unit output will start to decrease, ceteris puribus
Were
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
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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
Economic helps us to manager our limited resources, how to expand it, etc over unlimited want
Eagle
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
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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
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Kojo
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Emmanuel
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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
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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
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Junior
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Ogunsola
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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
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Awudu
discuss how international organization affect business
Imeobong
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
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