Three identical point masses of mass m each are placed at the vertices of an equilateral triangle and joined through springs of equal length and spring constant k . The system is placed on a smooth table. If the masses are displaced a little towards the centroid of the triangle then time period of oscillation of the system is :
F = -k x
ω = √(k/m)
The Attempt at a Solution
Consider one mass which is displaced from the mean position by x units. The two forces acting on it are k*x* cos(30 Degree) each inclined at an angle of 60 Degrees.
That would mean that the force acting on it is actually (3/2)*k*x, or the equivalent spring constant is (3/2)*k.
But that gives an weird time period which isn't in the options!