Edits to “Statement”, “Solution”, “Answer”

Artoghrul edited
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en/7.4.35.md +44 −4
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### Statement
−$7.4.35.$ What is the period of small vibrations of four charged bodies connected by identical filaments of length $l$ and moving as shown in the figure? Mass and charge of the body $m$ and $q$.
+$7.4.35.$ What is the period of small vibrations of four charged bodies connected by
+identical filaments of length l and moving as shown in the figure? Mass and
+charge of the body m and q.
−![For problem $7.4.35$|603x577, 30%](../../img/7.4.35/Screenshot_20250118_100131_Drive.jpg)
+![|603x577, 50%](../../img/7.4.35/Screenshot_20250118_100131_Drive.jpg)
+
+
### Solution
+The diagonal
+$$
+d=l\times\sqrt(2)
+$$
+$$
+d1=d+x
+$$
+$$
+F=k×q×q/(d1×d1)
+$$
+$$
+dF/dx=-2k×q×q/(d-x)\wedge3
+$$
−![Solution shared by @Artoghrul|2992x2007, 90%](../../img/7.4.35/img.jpg)
+k' is stifness of spring
+$$
+k'×dx=dF
+$$
+$$
+k'=2×k×q×q×dx/d\wedge3
+$$
+But the spring located between 2 object.We need period one of them
+
+The period formula
+$$
+T=2×\Pi×\sqrt(m/K)
+$$
+But the spring is between 2 object
+We need use half of spring
+so
+$$
+K=k'×2
+$$
+The period is
+$$
+T=2×\Pi×\sqrt(m×d\wedge3/(4×k×q×q))
+$$
+![|1637x1070, 50%](../../img/7.4.35/Screenshot_20250118_102946_Gallery.jpg)
#### Answer
$$
−T=2\pi\sqrt{4\pi\varepsilon_0ml^3/(\sqrt{2}q^2)}.
+T=2×\Pi×\sqrt(4×\Pi×\varepsilon×m×l×l/\sqrt(2)×q×q)
$$