Merge branch 'graph-interactivity' into 'main'

Added interactivity to Fig 3.3 of Chapter 3

See merge request !1

content/oscillations.md

@@ -246,6 +246,99 @@ glue("dampedoscillations", fig, display=False)
 Position as function of time for four types of oscillation: undamped ($\zeta = 0$, blue), underdamped ($0 < \zeta < 1$, orange), critically damped ($\zeta = 1$, green) and overdamped ($\zeta > 1$, red). In all cases the initial conditions are $x(0) = 1$ and $v(0) = 0$.
 ```
 
+
+```{code-cell} ipython3
+:tags: ["remove-input"]
+
+import numpy as np
+import plotly.graph_objects as go
+
+# Define parameters for the slider
+zeta_values = np.linspace(0, 2, 21)
+
+fig = go.Figure()
+
+# Function to determine color based on zeta value
+def get_color(zeta):
+    if zeta == 0:
+        return '#0f63a3'
+    elif 0 < zeta < 1:
+        return 'orange'
+    elif zeta == 1:
+        return 'green'
+    else:  # zeta > 1
+        return 'red'
+
+# Function to determine damping condition based on zeta value
+def get_damping_condition(zeta):
+    if zeta == 0:
+        return 'Undamped'
+    elif 0 < zeta < 1:
+        return 'Underdamped'
+    elif zeta == 1:
+        return 'Critically damped'
+    else:  # zeta > 1
+        return 'Overdamped'
+
+# Add traces for each zeta value
+for zeta in zeta_values:
+    t = np.linspace(0, 4*np.pi, 400)
+    if zeta == 0:
+        y = np.cos(t)
+    elif zeta < 1:
+        y = np.exp(-zeta*t) * np.cos(np.sqrt(1-zeta**2) * t)
+    elif zeta == 1:
+        y = (1 + t) * np.exp(-t)
+    else:  # zeta > 1
+        Omega = np.sqrt(zeta**2 - 1)
+        A = 0.5 + 1/(2*Omega)
+        B = 0.5 - 1/(2*Omega)
+        y = (A*np.exp((Omega - zeta) * t) + B*np.exp((-Omega - zeta) * t))
+    
+    color = get_color(zeta)
+    damping_condition = get_damping_condition(zeta)
+    fig.add_trace(go.Scatter(x=t, y=y, visible=False, name=f'ζ = {zeta:.2f} ({damping_condition})', line=dict(color=color)))
+
+# Make the first trace visible
+fig.data[0].visible = True
+
+# Create and add slider
+steps = []
+for i, zeta in enumerate(zeta_values):
+    damping_condition = get_damping_condition(zeta)
+    step = dict(
+        method="update",
+        args=[{"visible": [False] * len(zeta_values)},
+              {"title": f"Position as function of time for oscillation type: {damping_condition}"}],
+        label=f"{zeta:.2f}")
+    step["args"][0]["visible"][i] = True
+    steps.append(step)
+
+sliders = [dict(
+    active=0,
+    currentvalue={"prefix": "\u03B6 = "},
+    pad={"t": 50},
+    steps=steps
+)]
+
+fig.update_layout(
+    sliders=sliders,
+    title=f"Position as function of time for oscillation type: {get_damping_condition(zeta_values[0])}",
+    yaxis=dict(range=[-1, 1]),
+    xaxis=dict(
+        tickmode='array',
+        tickvals=[0, np.pi, 2*np.pi, 3*np.pi, 4*np.pi],
+        ticktext=['0', '\u03C0', '2\u03C0', '3\u03C0', '4\u03C0']
+    ),
+    xaxis_title='t',
+    yaxis_title='x(t)'
+)
+
+fig.show()
+
+```
+
+
 ## Driven harmonic oscillator
 
 ```{index} harmonic oscillator ; driven