<< Chapter < Page Chapter >> Page >
  • Describe a simple harmonic oscillator.
  • Explain the link between simple harmonic motion and waves.

The oscillations of a system in which the net force can be described by Hooke’s law are of special importance, because they are very common. They are also the simplest oscillatory systems. Simple Harmonic Motion (SHM) is the name given to oscillatory motion for a system where the net force can be described by Hooke’s law, and such a system is called a simple harmonic oscillator    . If the net force can be described by Hooke’s law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position, as shown for an object on a spring in [link] . The maximum displacement from equilibrium is called the amplitude     X size 12{X} {} . The units for amplitude and displacement are the same, but depend on the type of oscillation. For the object on the spring, the units of amplitude and displacement are meters; whereas for sound oscillations, they have units of pressure (and other types of oscillations have yet other units). Because amplitude is the maximum displacement, it is related to the energy in the oscillation.

Take-home experiment: shm and the marble

Find a bowl or basin that is shaped like a hemisphere on the inside. Place a marble inside the bowl and tilt the bowl periodically so the marble rolls from the bottom of the bowl to equally high points on the sides of the bowl. Get a feel for the force required to maintain this periodic motion. What is the restoring force and what role does the force you apply play in the simple harmonic motion (SHM) of the marble?

The figure a shows a spring on a frictionless surface attached to a bar or wall from the left side. On the right side of the spring, an object attached to it with mass m, its amplitude is given by X, and X is equal to zero at the equilibrium level. Force F is applied to it from the right side, shown with left direction pointed red arrow and velocity v is equal to zero. A direction point showing the north and west direction is also given alongside this figure as well as with other four figures. In figure b, after the force has been applied the object moves to the left compressing the spring a bit. And the displaced area of the object from its initial point is shown in sketched dots. The F here is equal to zero and the v is max in negative direction. In figure c, the spring has been compressed to the maximum level, and the amplitude is negative X. Now the direction of force changes to the rightward direction, shown with right direction pointed red arrow and the velocity v is zero. In figure d the spring is shown released from the compressed level and the object has moved toward the right side up to the equilibrium level. The F is zero, and the velocity v is maximum. In figure e the spring has been stretched loose to the maximum level and the object has moved to the far right. Now again the velocity here is equal to zero and the direction of force again is to the left hand side, shown here as F is equal to zero.
An object attached to a spring sliding on a frictionless surface is an uncomplicated simple harmonic oscillator. When displaced from equilibrium, the object performs simple harmonic motion that has an amplitude X size 12{X} {} and a period T size 12{T} {} . The object’s maximum speed occurs as it passes through equilibrium. The stiffer the spring is, the smaller the period T size 12{T} {} . The greater the mass of the object is, the greater the period T size 12{T} {} .

What is so significant about simple harmonic motion? One special thing is that the period T size 12{T} {} and frequency f size 12{f} {} of a simple harmonic oscillator are independent of amplitude. The string of a guitar, for example, will oscillate with the same frequency whether plucked gently or hard. Because the period is constant, a simple harmonic oscillator can be used as a clock.

Two important factors do affect the period of a simple harmonic oscillator. The period is related to how stiff the system is. A very stiff object has a large force constant k size 12{k} {} , which causes the system to have a smaller period. For example, you can adjust a diving board’s stiffness—the stiffer it is, the faster it vibrates, and the shorter its period. Period also depends on the mass of the oscillating system. The more massive the system is, the longer the period. For example, a heavy person on a diving board bounces up and down more slowly than a light one.

Questions & Answers

how may I solve arithmetic mean ,,,all example
Cee Reply
what is agriculture
Itoe Reply
simple method of understanding cost concept
Oludare Reply
what is inflation
Christiana Reply
Inflation is a general increase in price levels
is the action of inflating something
inflation is the persistent increase in general price level of goods and services in an economy over a considerable period of time .
inflation is the general increase of a commodity in a particular period of time.
inflation is a general increase in price levels of commodities
what are the types of inflation?
inflation is the period of persistent rise in the general level of the price of goods services over time
we have creeping inflation, demand pull inflation ,cost push inflation, and galloping inflation .
how can a location of a firm create difference between producers
joy Reply
what is monetary policy
is a monetary from policy that's authorized of country encharces
What would you say about the the mobility of enterprise as a factor of production?
Cathryn Reply
how can I connect myself to this Ambrose platform
kanu Reply
I am good and you I am from sierra Leone and I am new her
kanu Reply
u are welcome bro, here is a good platform for you to be
That i know,thanks bro.
what the main definition of economic
Uhara Reply
Essay about Microsoft
Kwena Reply
what is economics
Julie Reply
what do you mean by means in economics
economic is the wealth of a country.
monetary policy is refer to as being expansionary or contractionary.
pls who can help me to explain money market and capital market
money market is base on short term loan which is within one year period while capital market is long term loan more than one year...
money market is a market were short term loans are dealt with while capital market is a market were long term loans are traded
What is mean by monetory policy
monetary polices are rules that control the rate of monetary exchange in an economic as a whole.
wealth of the nation
important of unemployment
Otwe Reply
Important of unemployed
what is meaning scarcity
Scarcity can be define as human wants to goods,services,resources for exceed of what is available
hi guys
How are you
Can be defined as the inability to get everything we want
less ability for the available goods and services that's on sale
what is the definition of money market
what is consumer
Brenda Reply
how do consumer help people
by export trading
How do you mean Jayah
what is different between price and quantity
what is MRS
definition of economics according to Adam Smith
Ijeoma Reply
economic is a wealth of nation
in the view of Adam Smith economics is the study of activities of people in production of wealth
Economics is any human activity that lead to the provision of substance and or amassing wealth.
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 3

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Physics 110 at une. OpenStax CNX. Aug 29, 2013 Download for free at http://legacy.cnx.org/content/col11566/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics 110 at une' conversation and receive update notifications?