-
Home
- Waves and optics
- Oscillations in mechanical
- Damped oscillations
Add friction to a simple harmonic oscillator and see what happens.
Damped oscillations
Consider a simple harmonic oscillator that has friction, then the equations of
motion must be changed with the addition of a friction term. So we write
where
is the friction term. Rearranging we obtain:
or
Where
and
Assume a solution of form
substitute
into equation and get
so
must have real and imaginary parts, so rewrite:
So
the equation
becomes
upon substitution:
This
equation implies that the real and imaginary parts are each zero.Separatethe real and imaginary partsImaginary parts give:
From
Real parts get
or
Which
rearranges to
Thus
the solution becomes
where
Note that this has assumed a frictional damping force. For a more complicated
damping force, the result would be different.
Questions & Answers
evolutionary history and relationship of an organism or group of organisms
AI-Robot
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Waves and optics. OpenStax CNX. Nov 17, 2005 Download for free at http://cnx.org/content/col10279/1.33
Google Play and the Google Play logo are trademarks of Google Inc.