- #1
AntoineCompagnie
- 12
- 0
Homework Statement
A simple pendulum consists of a mass m suspended by a ball to a yarn (massless) of length l. We neglect friction forces.
Give the list of every forces applied to this system and then the motion of equation.
Why is the following equations necessary to find the motion equation true?I don't know where does the ##\alpha^2## comes from...
Homework Equations
\begin{align*}
\vec P + \vec T &=m\vec \alpha\\
\Leftrightarrow\begin{pmatrix}
{\vec ||P|| \cos \alpha}\\{- ||\vec P|| \sin \alpha}
\end{pmatrix}
+
\begin{pmatrix}
{-||\vec T||}\\{0}
\end{pmatrix}
&=
m\begin{pmatrix}
{l\alpha ^2}\\{l\alpha}
\end{pmatrix}
\end{align*}
Homework Statement
A simple pendulum consists of a mass m suspended by a ball to a yarn (massless) of length l. We neglect friction forces.
Give the list of every forces applied to this system and then the motion of equation.
Why is the following equations necessary to find the motion equation true?I don't know where does the ##\alpha^2## comes from...
Furthermore, I don't understand why the motion equation is found from the ##(2)## equation: ##\alpha + \frac{g\sin \alpha}{l}##.
Homework Equations
\begin{align*}
\vec P + \vec T &=m\vec \alpha\\
\Leftrightarrow\begin{pmatrix}
{\vec ||P|| \cos \alpha}\\{- ||\vec P|| \sin \alpha}
\end{pmatrix}
+
\begin{pmatrix}
{-||\vec T||}\\{0}
\end{pmatrix}
&=
m\begin{pmatrix}
{l\alpha ^2}\\{l\alpha}
\end{pmatrix}
\end{align*}
\begin{cases}
{m\vec g\cos \alpha - ||\vec T||= -ml\alpha^2}(1)\\
{- mg sin \alpha + 0 = ml\alpha} (2)
\end{cases}
The Attempt at a Solution
I tought That we would find the motion equation out from:
\begin{cases} mg + l \cos \alpha = 0\\ l \sin \alpha = 0 \end{cases}
from the fact that:
\begin{cases}
\vec T_x=(l\cos \alpha + mg) \vec i=\vec 0\\
\vec T_y=(l \sin \alpha) \vec j=\vec 0
\end{cases}
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