Updated spacing between @ latex expressions

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revision #10257 parent #9481 GitHub c702ebe ← older
en/3.1.8.md +3 −3
@@ -67,17 +67,17 @@
<h3>Solution</h3>
<p>
Newton's second law for the normal force of the Coulomb, which creates a restoring moment of force, is found in projection onto the vertical axis
−$$ ma_\tau=-qE\sin\varphi $$
+$$ ma_\tau =-qE\sin\varphi $$
Since the angle $\varphi$ is negligibly small, we will use $\sin\varphi\approx\varphi$
$$ -qE\varphi=-qE\frac{2x}{l} $$
From where we obtain the equation of harmonic oscillations
$$ m\ddot{x}(t)+\frac{2qE}{l}x(t)=0 $$
$$ \ddot{x}(t)+\frac{2qE}{ml}x(t)=0 $$
The solution to which we know:
−$$ \omega=\sqrt{\frac{2qE}{ml}} $$
+$$ \omega =\sqrt{\frac{2qE}{ml}} $$
From where, similarly to <a href="../3.1.6">3.1.6</a>, we find the maximum speed
−$$ \upsilon_0=x_0\omega=x_0\sqrt{\frac{2qE}{ml}} $$
+$$ \upsilon_0=x_0\omega =x_0\sqrt{\frac{2qE}{ml}} $$
After mathematical transformations we obtain the mass of the ball
$$ \boxed{m=\frac{2qEx_0^2}{l\upsilon_0^2}} $$
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