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Normal Modes

Normal Modes Screenshot  Download  Embed
  • Oscillator
  • Normal Modes
  • Polarization


  • Oscillator
  • Normal Modes
  • Polarization
  • Mass Spring System
  • Frequency
  • Amplitude
  • Phase


Play with a 1D or 2D system of coupled mass-spring oscillators. Vary the number of masses, set the initial conditions, and watch the system evolve. See the spectrum of normal modes for arbitrary motion. See longitudinal or transverse modes in the 1D system.

Sample Learning Goals

  • Explain what a normal mode is.
  • Explain what are the frequency, the amplitude, and the phase of a normal mode.
  • Explain why different normal modes have different frequencies and why higher-numbered modes have higher frequencies.
  • Identify how many normal modes a given system has and be able to sketch the individual modes qualitatively, for both 1D and 2D systems.
  • Explain the distinction between transverse and longitudinal normal modes in a 1D system.
  • Explain how adjusting the phase of a normal mode affects the motion of the system.
  • Explain qualitatively how any arbitrary state of the system can be written as a sum of normal modes; that is, explain the superposition principle.
  • Explain which properties of the system are set by the initial conditions, which properties are time-independent, and which properties are time-dependent.
  • Explain why striking a metal plate in one spot raises the temperature of the plate.
Version 1.01

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

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Language Download or Run Tips
Basque All Euskara Download Run now Bibrazio-modu normalak
Belarusian All беларускі Download Run now Нармальныя рэжымы
Bosnian All Bosanski Download Run now Normalni modovi
Chinese (Simplified) All 中文 (中国) Download Run now 标准振荡
Chinese (Traditional) All 中文 (台灣) Download Run now Normal Modes 正規振態
Danish All Dansk Download Run now Normalindstillinger
French All français Download Run now Modes vibratoires à plusieurs corps
Galician All Gallegan Download Run now Modos de vibración
German All Deutsch Download Run now Normalschwingungen 1D & 2D
Greek All Ελληνικά Download Run now Κανονικές καταστάσεις
Hebrew All עברית Download Run now מצבים נורמלים
Hungarian All magyar Download Run now Normál módusok
Indonesian All Bahasa Indonesia Download Run now Pola - pola Normal
Italian All italiano Download Run now Modi normali di vibrazione (Risonanza)
Japanese All 日本語 Download Run now 基準振動(モード)
Kannada All Kannada Download Run now ಲಂಭ ಬಹುವರ್ತಿ(ಮೋಡ್)
Kazakh All Kazakh Download Run now қалыпты тізімдер
Korean All 한국어 Download Run now 정규 모드
Macedonian All македонски Download Run now Нормални модови
Mongolian All Монгол (Монгол) Download Run now Хэвийн Горим
Persian All فارسی Download Run now مد طبيعي
Polish All polski Download Run now Mody Normalne
Portuguese (Brazil) All português (Brasil) Download Run now Modos Normais
Serbian All Српски Download Run now Нормални модови
Slovak All Slovenčina Download Run now Normálne vibračné módy
Spanish All español Download Run now Frecuencias resonantes. Download teacher tips PDF
Spanish (Mexico) All español (México) Download Run now Frecuencias resonantes. Download teacher tips PDF
Spanish (Peru) All español (Perú) Download Run now Frecuencias Resonantes
Thai All ไทย Download Run now โหมดปกติ
Turkmen All Turkmen Download Run now Yrgyldamanyň normal diapazonlary
Vietnamese All Tiếng Việt Download Run now Kiểu dao động chuẩn tắc

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Microsoft Windows
Macromedia Flash 9 or later
OS X 10.9.5 or later
Macromedia Flash 9 or later
Macromedia Flash 9 or later

Design Team Third-party Libraries Thanks To
  • Michael Dubson (lead designer/developer)
  • Jon Olson (developer)
  • Ariel Paul (development/interviews)
  • Trish Loeblein (development)