Two identical carts A and B each with mass m are connected via a spring with spring constant k. Two additional springs, identical to the first, connect the carts to two fixed points. The carts are free to oscillate under the effect of the springs in one dimensional frictionless motion.
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Under suitable initial conditions, the two carts will oscillate in phase according to
x_{\mathrm{A}}(t)=x_{0} \sin \omega_{1} t=x_{\mathrm{B}}(t)
where x_{\mathrm{A}} and x_{\mathrm{B}} are the locations of carts \mathrm{A} and \mathrm{B} relative to their respective equilibrium positions. Under other suitable initial conditions, the two carts will oscillate exactly out of phase according to
x_{\mathrm{A}}(t)=x_{0} \sin \omega_{2} t=-x_{\mathrm{B}}(t)
Determine the ratio \omega_{2} / \omega_{1}
Answer Choices
A. \sqrt{3}
B. 2
C. 2 \sqrt{2}
D. 3
E. 5
