Federschaltungen
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The following quantities appear in the problem:
Federkonstante \(D\) /
The following formulas must be used to solve the exercise:
\(D = D_1 + D_2 \quad \) \(\frac{1}{D} = \frac{1}{D_1} + \frac{1}{D_2} \quad \)
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Exercise:
In den folgen Darstellungen haben die enquotedicken Federn eine Federkonstante von DaO und die enquotedünnen Federn eine solche von DbO. Berechne jeweils die Ersatzfederkonstante für das gesamte Gebilde! center tikzpicture scope drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--.; scope scopexshiftcm drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope scopexshiftcm drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate .--; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope scopexshiftcm drawultra thick --; drawultra thick --; % unterer Zweig: eine dicke Feder drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; % oberer Zweig: zwei dünne Federn in Reihe drawdecorationaspect. segment length.mm amplitudemmcoildecorate --.; drawultra thick ..--..; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope tikzpicture center
Solution:
abcliste abc Die Ersatzfederkonstante ist SolQtyaD/*DaX+/DbX^-Npm Ders leftfracD_+D_+fracD_right^- leftfracDa+Da+fracDbright^- aDP abc Die Ersatzfederkonstante ist SolQtybD/DaX+/DbX^-+DaXNpm Ders leftfracD_+fracD_right^-+D_ leftfracDa+fracDbright^-+Da bDP abc Die Ersatzfederkonstante ist SolQtycD/DaX+/DbX^-+/DaX+/DbX^-Npm Ders leftfracD_+fracD_right^-+leftfracD_+fracD_right^- leftfracDa+fracDbright^-+leftfracDa+fracDbright^- cDP abc Die Ersatzfederkonstante ist abcliste
In den folgen Darstellungen haben die enquotedicken Federn eine Federkonstante von DaO und die enquotedünnen Federn eine solche von DbO. Berechne jeweils die Ersatzfederkonstante für das gesamte Gebilde! center tikzpicture scope drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--.; scope scopexshiftcm drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope scopexshiftcm drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate .--; drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --.; drawultra thick --; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope scopexshiftcm drawultra thick --; drawultra thick --; % unterer Zweig: eine dicke Feder drawdecorationaspect. segment lengthmm amplitudemmcoildecorate --; % oberer Zweig: zwei dünne Federn in Reihe drawdecorationaspect. segment length.mm amplitudemmcoildecorate --.; drawultra thick ..--..; drawdecorationaspect. segment length.mm amplitudemmcoildecorate .--; scope tikzpicture center
Solution:
abcliste abc Die Ersatzfederkonstante ist SolQtyaD/*DaX+/DbX^-Npm Ders leftfracD_+D_+fracD_right^- leftfracDa+Da+fracDbright^- aDP abc Die Ersatzfederkonstante ist SolQtybD/DaX+/DbX^-+DaXNpm Ders leftfracD_+fracD_right^-+D_ leftfracDa+fracDbright^-+Da bDP abc Die Ersatzfederkonstante ist SolQtycD/DaX+/DbX^-+/DaX+/DbX^-Npm Ders leftfracD_+fracD_right^-+leftfracD_+fracD_right^- leftfracDa+fracDbright^-+leftfracDa+fracDbright^- cDP abc Die Ersatzfederkonstante ist abcliste