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F = ma (Final Problems)
Simple Harmonic Motion
FMA-2015-25 · 2015 F = ma (AAPT)

2015 F = ma Exam — Question 25

25. 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. Cart A Cart B Under suitable initial conditions, the two carts will oscillate in phase according to xA(t) = x0 sin ω1t = xB(t) where xA and xB are the locations of carts A and B relative to their respective equilibrium positions. Under other suitable initial conditions, the two carts will oscillate exactly out of phase according to xA(t) = x0 sin ω2t = −xB(t) Determine the ratio ω2/ω1 √
Source: Question 25, 2015 F = ma Exam, © 2015 American Association of Physics Teachers (AAPT) and the U.S. Physics Team. Adapted by PhysicsTrainer: reformatted into a separate question and answer choices for online multiple-choice practice; any shared setup from nearby questions is repeated here. Not affiliated with or endorsed by AAPT or the U.S. Physics Team.