Z3

doc/main.tex

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+\documentclass{article}
+\usepackage{amsmath}
+
+\begin{document}
+
+The velocity of the mass as a function of time \( t \) is described by the equation:
+
+\[
+v(t) = v_{\text{max}} \cdot \sin(\omega t + \phi)
+\]
+
+where:
+\begin{itemize}
+    \item \( v_{\text{max}} \) is the maximum velocity (amplitude of velocity),
+    \item \( \omega \) is the angular frequency of the oscillations,
+    \item \( \phi \) is the initial phase.
+\end{itemize}
+
+The angular frequency \( \omega \) is related to the period \( T \) by the formula:
+
+\[
+\omega = \frac{2\pi}{T}
+\]
+
+For a period \( T = 0.4 \) seconds:
+
+\[
+\omega = \frac{2\pi}{0.4} = 5\pi \, \text{rad/s}
+\]
+
+If the mass starts moving from the equilibrium position with an upward velocity, the initial phase \( \phi \) is 0. Then, the velocity equation becomes:
+
+\[
+v(t) = 0.8 \cdot \sin(5\pi t)
+\]
+
+\end{document}