update theo and proseminar

2020-04-29 21:43:16 +02:00
parent 7fe281e6aa
commit 92d3b35535
4 changed files with 25 additions and 6 deletions
@@ -107,9 +107,10 @@
                \intertext{Zusammen folgt}
                &\Delta t = \int_{x_0}^{x_E} \frac{\sqrt{1 + f'(x)^2}}{\sqrt{\frac{2}{m} (E - V(\vec{x}))}} \d x
            .\end{align*}
-        \item Mit $E = 0$, $x_0 = 0$, $x_E = 1$ und $f(x) = x$ folgt
+        \item Mit $V(z) = mgz$, $E = 0$, $x_0 = 0$, $x_E = 1$ und $f(x) = x$ folgt
            \[
-            \Delta t = \int_{0}^{1} \frac{\sqrt{2} }{\sqrt{2 g} } \d x = \frac{2}{\sqrt{g} } \sqrt{x}
+            \Delta t = \int_{0}^{1} \frac{\sqrt{2} }{\sqrt{\frac{2}{m} mgx} } \d x
+            = \int_{0}^{1} \frac{\sqrt{2} }{\sqrt{2 g x} } \d x = \frac{2}{\sqrt{g} } \sqrt{x}
            \Big|_{0}^{1} = \frac{2}{\sqrt{g} }
            .\] 
    \end{enumerate}