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Conceptual questions

What conditions must be met to produce simple harmonic motion?

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(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?

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

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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.

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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.

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

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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 . 37 N/m size 12{2 "." "37"`"N/m"} {}

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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?

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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

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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?

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Suppose you attach the object with mass m size 12{"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 mg on the object at its lowest point. (b) If the spring has a force constant of 10 . 0 N/m size 12{"10" "." 0`"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.

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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

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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?

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The figure shows a little kid, about ten to twelve months old, standing in a toy jolly jumper, which is tied to the ceiling hook by its four spring belts.
This child’s toy relies on springs to keep infants entertained. (credit: By Humboldthead, Flickr)

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?

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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] .

The figure shows two skydivers midway through the air, with both with open having their parachutes open.
The oscillations of one skydiver are about to be affected by a second skydiver. (credit: U.S. Army, www.army.mil)

1.94 s

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Questions & Answers

Describe an experiment to determine short half life
Tyson Reply
what is science
Kenedy Reply
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
Musa Reply
what is physics
Caya Reply
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
it is when you get up of your arse and do some real work 😁
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Eden Reply
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
what are the fundamentals qualities
Magret Reply
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
Ekwunazor Reply
your fat arse sitting all day is a good reference of three dimensional numbnut
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
Lathan Reply
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
Ochigbo Reply
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
Lord Reply
you mean in three dimensions......numbnut
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
time seems to flow in one direction...but I the past present and future happen every moment time flies regardless.
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman
if v=ktx Ly Mz find the value of x,y and z
Emmanuel Reply
x=v=ktx Ly Mz find the value of x,y and z
y=v=ktx Ly Mz find the value of x,y and z
z=v=ktx Ly Mz find the value of x,y and z
now get your lazy arse up and clean the kitchen 😁
I want to join the conversation
Subaba Reply
😂
hmm
Stephen
what conversation you talking about? .....numbnut
how do i calculate for period of the oscillation
Bridget Reply
T=2π√(m÷k).K is spring constance
Ambe
T=2π√m/k
Lord
does the force in a system result in the energy transfer?
Lebatam Reply
full meaning of GPS system
Anaele Reply
global positioning system
Noman
what's the use of the GPS
Matthew
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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