Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Harmonic oscillator
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
===Step input=== {{See also|Step response}} In the case {{math|''ΞΆ'' < 1}} and a unit step input with {{math|1=''x''(0) = 0}}: <math display="block"> \frac{F(t)}{m} = \begin{cases} \omega _0^2 & t \geq 0 \\ 0 & t < 0 \end{cases}</math> the solution is <math display="block"> x(t) = 1 - e^{-\zeta \omega_0 t} \frac{\sin \left( \sqrt{1 - \zeta^2} \omega_0 t + \varphi \right)}{\sin(\varphi)},</math> with phase ''Ο'' given by <math display="block">\cos \varphi = \zeta.</math> The time an oscillator needs to adapt to changed external conditions is of the order {{math|1=''Ο'' = 1/(''ΞΆΟ''<sub>0</sub>)}}. In physics, the adaptation is called [[relaxation (physics)|relaxation]], and ''Ο'' is called the relaxation time. In electrical engineering, a multiple of ''Ο'' is called the ''settling time'', i.e. the time necessary to ensure the signal is within a fixed departure from final value, typically within 10%. The term ''overshoot'' refers to the extent the response maximum exceeds final value, and ''undershoot'' refers to the extent the response falls below final value for times following the response maximum.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)