From 3e3e4938cc53ce5ee542c8571d6008e50e727d42 Mon Sep 17 00:00:00 2001 From: Roger Wolf <roger.wolf@kit.edu> Date: Mon, 21 Oct 2024 09:32:12 +0200 Subject: [PATCH] clafirying and fixing a few items --- Pendel/Datenblatt.md | 2 +- Pendel/doc/Hinweise-Reversion-Auswertung.md | 14 +++++++------- Pendel/figures/Reversionspendel.odg | Bin 2772602 -> 2772730 bytes Pendel/figures/Reversionspendel.png | Bin 1086918 -> 1088930 bytes 4 files changed, 8 insertions(+), 8 deletions(-) diff --git a/Pendel/Datenblatt.md b/Pendel/Datenblatt.md index 53ae4d0..1f3cc2f 100644 --- a/Pendel/Datenblatt.md +++ b/Pendel/Datenblatt.md @@ -11,7 +11,7 @@ Für den Versuch stehen Ihnen die folgenden Apparaturen und Materialien zur Verf - Dichte $\rho=4.94\ \mathrm{g/cm}$. - Durchmesser $L=(1.500\pm0.02)\ \mathrm{cm}$ - Die Massen der Auflagekeile hängen vom verwendeten Pendel ab: - - Für **R1** $m_{\mathrm{K}}^{\mathrm{P1}}=(86.0\pm0.5)\ \mathrm{g},\ m_{\mathrm{K^{\prime}}}^{\mathrm{P1}}=(72.0\pm0.5)\ \mathrm{g}.$ + - Für **R1** $m_{\mathrm{K}}^{\mathrm{P1}}=(72.0\pm0.5)\ \mathrm{g},\ m_{\mathrm{K^{\prime}}}^{\mathrm{P1}}=(86.0\pm0.5)\ \mathrm{g}.$ - Für **P2** $m_{\mathrm{K}}^{\mathrm{P2}}=m_{\mathrm{K^{\prime}}}^{\mathrm{P2}}=(83.0\pm0.5)\ \mathrm{g}$. - Die Entfernung des Auflagepunkts A (A') vom Rand der jeweiligen Montagespange beträgt $\Delta=(1.00\pm0.02)\ \mathrm{cm}$. - Der verschiebbare Keil K' ist um $90^{\circ}$ gegen den festen Keil K gedreht. diff --git a/Pendel/doc/Hinweise-Reversion-Auswertung.md b/Pendel/doc/Hinweise-Reversion-Auswertung.md index e10584b..c2dc0e7 100644 --- a/Pendel/doc/Hinweise-Reversion-Auswertung.md +++ b/Pendel/doc/Hinweise-Reversion-Auswertung.md @@ -28,27 +28,27 @@ D(d_{i}) = T_{0}(d_{i})-T_{0}'(d_{i}) $$ auf. Passen Sie an diese Datenreihe das Modell für $T_{0}'$ aus Gleichung **(1)** an. -Aus der folgenden Rechnung können Sie sich leicht überzeugen, dass Sie für $D(d_{i})$ den gleichen funktionalen Zusammenhang mit $d$, wie für $T_{0}'$ erwarten: +Aus der folgenden Rechnung können Sie sich leicht überzeugen, dass Sie für $D(d_{i})$ den gleichen quadratischen Zusammenhang als Funktion von $d$, wie für $T_{0}'$ erwarten: $$ \begin{equation*} \begin{split} D(d) &= T_{0}(d) - T_{0}'(d);\\ &\\ -& = \bigl(\beta'\,d + \gamma'\bigr) - \bigl(\alpha\,d^{2} + 2\alpha\beta\,d + \left(\beta^{2}+\gamma\right)\bigr);\\ +& = \bigl(\beta'\,d + \gamma'\bigr) - \bigl(\alpha\,d^{2} - 2\alpha\beta\,d + \left(\alpha\,\beta^{2}+\gamma\right)\bigr);\\ &\\ -& = \alpha\,d^{2} + \underbrace{(\beta'-2\alpha\beta)}\,d + \underbrace{\left(\gamma'-\left(\beta^{2}+\gamma\right)\right)}\\ -&\hphantom{= \alpha\,d^{2} +\beta'-} \equiv\widetilde{\beta} +& = -\alpha\,d^{2} + \underbrace{(\beta'+2\alpha\,\beta)}\,d + \underbrace{\left(\gamma'-\left(\alpha\,\beta^{2}+\gamma\right)\right)}\\ +&\hphantom{= -\alpha\,d^{2} +\beta'-} \equiv\widetilde{\beta} \hphantom{\beta + \gamma'-\beta^{2}+}\equiv\widetilde{\gamma}\\ \end{split} \end{equation*} $$ -Aus dem Modell für $T_{0}'$ aus Gleichung **(1)** können Sie $\ell_{r}$ leicht mit Hilfe der folgenden Umstellung +Mit der gleichen Parameterwahl, wie für das Modell für $T_{0}'$ aus Gleichung **(1)** können Sie $\ell_{r}$ leicht mit Hilfe der folgenden Umstellung $$ \begin{equation*} \begin{split} -& D(\ell_{r}) = \alpha\,(\ell_{r}-\beta)^{2} + \gamma = 0; \\ +& D(\ell_{r}) = \hat{\alpha}\,(\ell_{r}-\hat{\beta})^{2} + \hat{\gamma} = 0; \\ &\\ -& \ell_{r} = \pm\sqrt{-\frac{\gamma}{\alpha}}+\beta +& \ell_{r} = \pm\sqrt{-\frac{\hat{\gamma}}{\hat{\alpha}}}+\hat{\beta} \end{split} \end{equation*} $$ diff --git a/Pendel/figures/Reversionspendel.odg b/Pendel/figures/Reversionspendel.odg index 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