# 16.3 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

When a toilet is flushed or a sink is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the northern hemisphere.
find the change in entropy of a 2.00 kg block of gold at 1063^0C when it meets to become liquid gold at 1063^0C
if you are asked to make a very sensitive thermometer which of the following fluids would you choose
precious
between mercy and gasoline
precious
it good to use mercury because mercury does not wet glass and it does not evaporate easily
Desmond
0
firdaus
SFAR Sifar SIFAT -<SIFST
firdaus
how many particles are in 2 moles of chromium
if so use the normal formula number of atom= number of particle/Avogadro's number
Aki
n= np/avogadtos constant. therefore n= 24/ 6.022×10²³
albert
24÷6.022×10²³
albert
@Albert is wrong
Aki
when you cross multiple it should give you Number of particles= mole*Avogadro's number X=2m*6.022*10^²³ X=1.20*10²⁴g
Aki
1.204×10^-22
Maame
please what is final velocity and initial velocity
don't know
Ekene
what do you want to become in future
Ekene
Nonso
I think initial velocity is the velocity that the mobile starts with at the start time (t=0s) but I don't think I heard abt final velocity
Malak
Malak where are you now I need to learn more from you
Ekene
initial velocity is the velocity an object possess at it intial position or is the starting velocity, while a final velocity is the velocity an object or body possess at it final stage or at the end of it motion
Mubarak
Bohr is kimia, of toksid, cloud, tree have cloud, tree, river but small from toksid fish or another.
Heavy, heavy kehidupan susah, kekayaan, berlambak, bergumpul. Dikenali.
Gravitional, Gravitional mean kehidup seseorang. Kehidupan bumi, kehidupan muka bumi, kehidupan dalam longitude, kehidupan dalam momentom, kehidupan dalam mongitude. Kehidupan dalam Pelajaran, mean Pelajar kolej.
firdaus
Nonconservative. Sains belajar
firdaus
hello
LFX
what are the types of kinetics
what is torque pls
An aluminum rod of length 1.8cm at 0°C is heated to produced a difference in length of 0.007cm. Calculate the temperature to which it is heated. Take the linear expansively aluminun as 2.3×10^-5 K^-1.
apply the formula... linear expansivity... everything you need are in the question already
Aki
Guys pls who understand equilibrium of forces mostly the calculation aspect
Faith
so can u explain how to solve the calculations
Faith
CcmT 0°0°M°T 4°4°0°0 4400°c Right Calculate 4400c Don't have rules with him
firdaus
please can someone explain how coulombs law is used to determine electric force
u know coulomb's law and electric force are related in a formula which is E=f/q where E is equals to electric field intensity and f is equals to the force while-q is equals to the charge
Juilet
and I guess no the formula for electric field intensity
Juilet
and I guess you know the formula for electric field intensity
Juilet
exactly what i want to say
Haruna
Field mean like don't have we give have.. Yap... That oil Airplan. Dshell n petrol..
firdaus
what is momentum
Momentum mean bacteria... OR CARE MONEY FROM STOLED.. OR CARE WE PLACE OR HOME FROM STOLED OR CARE WE BODY FROM STOLED
firdaus
Moment
firdaus
let him explain the statement well
Hello guys I'm new here
diewgatdet
hello
Godwin
Statement is resit, temu bual.
firdaus
the specimens of different materials can have same if their dimensions don't match a) resistance b) resistivity c) both d) statement is ambiguous
shoukat
b
diewgatdet
Bacteria.
firdaus
Specimen mean super human.. Power hin
firdaus
, yap like that lag
firdaus
please someone should help me with the Archimedes principle
Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics.
Destiny
Have you heard of quantum fluctuations?
Or quanta
Hkekuasa human
firdaus
hello
LFX
It states that the body of a substance is partially wholly, when initially imirssed, lower in to a fluid liquid or gas, the expression upthrust which is equal to the body of the fluid displaced. But bouncy is the upward force in which a body suppressed upon a submerged body.
albert
it states that when a body is fully or partially immersed in a fluid, it experiences an upward force known as upthrust which is equal to the weight of fluid displaced.
Maame
Understanding the periodic table
Mean kapsul don't have.. We do... Black kapsul
firdaus
We use tree. Any.. To be black
firdaus