diff --git a/src/presentation/main.md b/src/presentation/main.md
index 2c0798c..8a9fa17 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,8 +7,41 @@
 
 ### Die harmonische Schwingung
 
-$$ F = -D * s $$
-$$ \frac{d v}{dt} = \frac{F}{m} $$
+$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$
+;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$
+;$$\omega = \sqrt{\frac{D}{m}}$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$
+;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$
+;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+
+$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$
+$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{ges} = \frac{1}{2} * D * A^2 $$
+
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix}
+A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t)
+= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t)$$
+;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$
 
 ---
 

diff --git a/src/presentation/main.md b/src/presentation/main.md
index 2c0798c..8a9fa17 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,8 +7,41 @@
 
 ### Die harmonische Schwingung
 
-$$ F = -D * s $$
-$$ \frac{d v}{dt} = \frac{F}{m} $$
+$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$
+;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$
+;$$\omega = \sqrt{\frac{D}{m}}$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$
+;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$
+;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+
+$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$
+$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{ges} = \frac{1}{2} * D * A^2 $$
+
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix}
+A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t)
+= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t)$$
+;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$
 
 ---
 
diff --git a/src/python/oscillator.py b/src/python/oscillator.py
index f38846c..c2885de 100644
--- a/src/python/oscillator.py
+++ b/src/python/oscillator.py
@@ -7,8 +7,8 @@
 omega = 2*np.pi * 0.25
 A = 1
 
-position = lambda t: A*np.sin(omega * t)
-speed = lambda t: A*np.cos(omega*t)
+position = lambda t: A*np.cos(omega * t)
+speed = lambda t: A*np.sin(omega*t)
 
 totalTime = 12
 framerate = 20
@@ -19,14 +19,14 @@
 diagrammAx.set_ylim(-1.5*A, 1.5*A)
 diagrammAx.set_xlim(-1.5*A, 1.5*A)
 diagrammAx.set_xlabel("x")
-diagrammGraph,  = diagrammAx.plot([0, 0], [0, 0], "o-")
+diagrammGraph,  = diagrammAx.plot([0, 1], [0, 0], "o-")
 
 phaseSpaceAx.axis("equal")
 phaseSpaceAx.set_ylim(-1.5*A, 1.5*A)
 phaseSpaceAx.set_xlim(-1.5*A, 1.5*A)
 phaseSpaceAx.set_xlabel("x")
 phaseSpaceAx.set_ylabel("v")
-phaseGraph, = phaseSpaceAx.plot([0, 0], [0, 1], "o-")
+phaseGraph, = phaseSpaceAx.plot([0, 0], [0, 0], "o-")
 
 positionAx.set_xlim(-1.5*A, 1.5*A)
 positionAx.set_ylim(0, totalTime)

diff --git a/src/presentation/main.md b/src/presentation/main.md
index 2c0798c..8a9fa17 100644
--- a/src/presentation/main.md
+++ b/src/presentation/main.md
@@ -7,8 +7,41 @@
 
 ### Die harmonische Schwingung
 
-$$ F = -D * s $$
-$$ \frac{d v}{dt} = \frac{F}{m} $$
+$$ a = \frac{d v}{dt} = \frac{F}{m} = -\frac{D*x}{m} = \frac{d^2 x}{d^2 t}$$
+;$$ x = A*\cos(\omega * t) \Leftrightarrow \frac{d^2 x}{d^2 t} = -\frac{D*x}{m} = -\omega^2 * x $$
+;$$\omega = \sqrt{\frac{D}{m}}$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ x = A*\cos(\sqrt{\frac{D}{m}} * t) $$
+;$$ v = \frac{d x}{d t} = \omega * A * \sin(\sqrt{\frac{D}{m}} * t)$$
+;$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+;$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{kin} = \frac{1}{2} * m * v^2 = \frac{1}{2} * D * A^2 * \sin^2(\omega * t)$$
+
+$$ E_{Feder} = \frac{1}{2} * D * x^2 = \frac{1}{2} * D * A^2 * \cos^2(\omega * t)$$
+
+;$$ E_{ges} = E_{kin} + E_{Feder} = \frac{1}{2} * D * A^2 * $$
+$$(\sin^2(\omega * t) + \cos^2(\omega * t)) = \frac{1}{2} * D * A^2 $$
+
+---
+
+### Die harmonische Schwingung
+
+$$ E_{ges} = \frac{1}{2} * D * A^2 $$
+
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} x \\ \frac{v}{\omega} \end{pmatrix} = \sqrt{\frac{D}{2}}*\begin{pmatrix}
+A*\cos(\omega * t) \\ \frac{\omega * A * \sin(\omega * t)}{\omega}\end{pmatrix}$$
+;$$ \Psi = \sqrt{\frac{D}{2}}*\begin{pmatrix} A \\ A \end{pmatrix} \odot \circlearrowleft(\omega * t)
+= \sqrt{\frac{D}{2}}*A *\circlearrowleft(\omega * t)$$
+;$$|\Psi|^2 = E_{ges} = \frac{D*A^2}2 $$
 
 ---
 
diff --git a/src/python/oscillator.py b/src/python/oscillator.py
index f38846c..c2885de 100644
--- a/src/python/oscillator.py
+++ b/src/python/oscillator.py
@@ -7,8 +7,8 @@
 omega = 2*np.pi * 0.25
 A = 1
 
-position = lambda t: A*np.sin(omega * t)
-speed = lambda t: A*np.cos(omega*t)
+position = lambda t: A*np.cos(omega * t)
+speed = lambda t: A*np.sin(omega*t)
 
 totalTime = 12
 framerate = 20
@@ -19,14 +19,14 @@
 diagrammAx.set_ylim(-1.5*A, 1.5*A)
 diagrammAx.set_xlim(-1.5*A, 1.5*A)
 diagrammAx.set_xlabel("x")
-diagrammGraph,  = diagrammAx.plot([0, 0], [0, 0], "o-")
+diagrammGraph,  = diagrammAx.plot([0, 1], [0, 0], "o-")
 
 phaseSpaceAx.axis("equal")
 phaseSpaceAx.set_ylim(-1.5*A, 1.5*A)
 phaseSpaceAx.set_xlim(-1.5*A, 1.5*A)
 phaseSpaceAx.set_xlabel("x")
 phaseSpaceAx.set_ylabel("v")
-phaseGraph, = phaseSpaceAx.plot([0, 0], [0, 1], "o-")
+phaseGraph, = phaseSpaceAx.plot([0, 0], [0, 0], "o-")
 
 positionAx.set_xlim(-1.5*A, 1.5*A)
 positionAx.set_ylim(0, totalTime)
diff --git a/src/template_presentation.html b/src/template_presentation.html
index 94d4c37..3df0e52 100644
--- a/src/template_presentation.html
+++ b/src/template_presentation.html
@@ -18,7 +18,11 @@
   <script defer src="https://cdn.jsdelivr.net/npm/katex@0.11.1/dist/contrib/auto-render.min.js"
     integrity="sha384-kWPLUVMOks5AQFrykwIup5lo0m3iMkkHrD0uJ4H5cjeGihAutqP0yW0J6dpFiVkI" crossorigin="anonymous"
     onload="renderMathInElement(document.body);"></script>
-
+  <style>
+    .katex-display {
+      scale: 80%;
+    }
+  </style>
 </head>
 
 <body class="reveal">