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 2 l. What is the spring constant k of the springs?
Answer Choices
A. 2 m \omega^{2}
B. \frac{2}{\sqrt{3}} m \omega^{2}
C. \frac{2}{3} m \omega^{2}
D. \frac{1}{\sqrt{3}} m \omega^{2}
E. \frac{1}{3} m \omega^{2}