STEMS 2021 Phy Cat B Q2
Source:
January 23, 2021
Problem Statement
A regular tetrahedral massless frame whose side length is physically variable (with the constraint of the tetrahedron being regular) is dipped in a soap solution of surface tension , taken outside and allowed to settle after a little wiggle.\\
The soap film is formed such that there is no volume in space that is enclosed by any of the surfaces soap film and all the soap film surfaces are planar. You may assume the configuration of the soap film without proof.\\
Now 4 point charges of charge are fixed at the vertices of the tetrahedron.\\
The system now sets into motion with the shape and nature of soap film being unaltered at all times.\\ [*] Find the side length of the tetrahedron for which the system attains mechanical equilibrium. [/*]
[*] Find the differential equation(s) governing the side length with respect to time.[/*]
[*] If the amplitude of oscillations are very small, find the time period of oscillations.[/*]