Difference between revisions of "The research of simple linear vibrating system"

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[[Виртуальная лаборатория]] > [[Исследование простейшей линейной колебательной системы]] <HR>
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[[Virtual laboratory]] > [[The research of simple linear vibrating system]] <HR>
  
 
<math>
 
<math>
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\def\){\right)}
 
\def\){\right)}
 
</math>
 
</math>
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Здесь расположена программа, демонстрирующая зависимость скорости от перемещения грузика на линейной пружине.
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Here is the program showing the dependence of the speed of movement of the sinker on a linear spring.  
  
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Для начала, получим данную зависимость. Запишем закон Гука:
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For starters to get this dependency. We write the Hooke's law:
 
::<math>
 
::<math>
 
F = - Cu,
 
F = - Cu,
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</math>
 
</math>
  
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Поделим на <math>m</math> и умножим на <math>\dot u</math>:
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Divide by  <math>m</math> and multiply by <math>\dot u</math>:
 
::<math>
 
::<math>
 
\ddot u \dot u + \omega^2 \dot u u = 0, \quad \omega_0 \MYdef \sqrt{\frac{C}{m}},
 
\ddot u \dot u + \omega^2 \dot u u = 0, \quad \omega_0 \MYdef \sqrt{\frac{C}{m}},
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</math>
 
</math>
  
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Введем обозначения:
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We introduce the notation:
 
::<math>\frac{\dot u}{\omega} = y, \quad u = x</math>.
 
::<math>\frac{\dot u}{\omega} = y, \quad u = x</math>.
  
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Получим формулу круга:
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We get the formula of the circle:
 
<math> y^2 + x^2 = 0 </math>.
 
<math> y^2 + x^2 = 0 </math>.
  
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Данная зависимость видна на графике в программе:
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This dependence is visible on the chart in the program:
  
 
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Spring/New_spring_v1.3_no_constructor/draw_spring.html |width=830 |height=550 |border=0 }}
 
{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Tcvetkov/Spring/New_spring_v1.3_no_constructor/draw_spring.html |width=830 |height=550 |border=0 }}
  
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Разработчики: [[Цветков Денис]], [[Кривцов Антон]].
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Developers: [[D.V. Tsvetkov]], [[A.M. Krivtsov]].
  
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[[Category: Виртуальная лаборатория]]
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[[Category: Virtual laboratory]]
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[[Category: Программирование]]
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[[Category: Programming]]
 
[[Category: JavaScript]]
 
[[Category: JavaScript]]

Latest revision as of 08:36, 3 June 2016

Virtual laboratory > The research of simple linear vibrating system

[math] \def\MYdef{\mathrel{\stackrel{\rm def}=}} \def\({\left(} \def\){\right)} [/math] Here is the program showing the dependence of the speed of movement of the sinker on a linear spring.

For starters to get this dependency. We write the Hooke's law:

[math] F = - Cu, [/math]
[math] m \ddot u + Cu = 0. [/math]

Divide by [math]m[/math] and multiply by [math]\dot u[/math]:

[math] \ddot u \dot u + \omega^2 \dot u u = 0, \quad \omega_0 \MYdef \sqrt{\frac{C}{m}}, [/math]
[math] \dot u^2 + \omega^2 u^2 = 0, \quad \(x^2(t)\)'_t = 2x(t)\dot u(t), [/math]
[math] \(\frac{\dot u}{\omega}\)^2 + u^2 = 0. [/math]

We introduce the notation:

[math]\frac{\dot u}{\omega} = y, \quad u = x[/math].

We get the formula of the circle: [math] y^2 + x^2 = 0 [/math].

This dependence is visible on the chart in the program:

Developers: D.V. Tsvetkov, A.M. Krivtsov.

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