Equilateral Spring Triangle

Level pending

Three point masses \( m \) are attached together by identical springs. When placed at rest on a horizontal surface the masses form a triangle with side length \( l \). When the assembly is rotated about its center at angular velocity \( \omega \), the masses form a triangle with side length \( 2l \). What is \( \dfrac{k}{m\omega^2} \) for the springs, if \( k \) is the spring constant?

Note: A version of this problem appeared on the 2012 F = ma exam.

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