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Examples of harmonic motion are :

  • x = A e - ω t sin ω t
  • x = A sin ω t
  • x = A ω cos ω t
  • x = A sin ω t + B cos ω t

Of these, last three examples are simple harmonic oscillations.

Note that we can reduce fourth example, sum of two trigonometric functions, into a single trigonometric function with appropriate substitutions. As a matter of fact, we shall illustrate such reduction in appropriate context.

The simple harmonic oscillation is popularly known as simple harmonic motion (SHM). The important things to reemphasize here is that SHM denotes an oscillation, which does not involve change in amplitude. We shall learn that this represents a system in which energy is not dissipated. It means that mechanical energy of a system in SHM is conserved.

Non-harmonic oscillation

A non-harmonic oscillation is one, which is not harmonic motion. We can consider combination of two or more harmonic motions of different frequencies as an illustration of non-harmonic function.

x = A sin ω t + B sin 2 ω t

We can not reduce this sum into a single trigonometric sine or cosine function and as such, motion described by the function is non-harmonic.

Simple harmonic motion

A simple harmonic motion can be conceived as a “to and fro” motion along an axis (say x-axis). In order to simplify the matter, we choose origin of the reference as the point about which particle oscillates. If we start our observation from positive extreme of the motion, then displacement of the particle “x” at a time “t” is given by :

x = A cos ω t

where “ω” is angular frequency and “t” is the time. The figure here shows the positions of the particle executing SHM at an interval of “T/8”. The important thing to note here is that displacements in different intervals are not equal, suggesting that velocity of the particle is not uniform. This also follows from the nature of cosine function. The values of cosine function are not equally spaced with respect to angles.

Simple harmonic motion

Positions of the particles at different times are shown.

Amplitude

We know that value of cosine function lies between “-1” and “1”. Hence, value of “x” varies between “-A” and “A”. If we plot the function describing displacement, then the plot is similar to that of cosine function except that its range of values lies between “-A” and “A”.

Amplitude

The scalar value of maximum displacement from the mean position is known as the amplitude of oscillation.

The value “A” denotes the maximum displacement in either direction. The scalar value of maximum displacement from the mean position is known as the amplitude of oscillation. If we consider pendulum, we can observe that farther is the point from which pendulum bob (within the permissible limit in which the bob executes SHM) is released, greater is the amplitude of oscillation. Similarly, greater is the stretch or compression in the spring executing SHM, greater is the amplitude. Alternatively, we can say that greater is the force causing motion, greater is the amplitude. In the nutshell, amplitude of SHM depends on the initial conditions of motion - force and displacement.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Oscillation and wave motion. OpenStax CNX. Apr 19, 2008 Download for free at http://cnx.org/content/col10493/1.12
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