Two equal masses on an effectively friction less horizontal air track are held between rigid supports by three identical springs, as shown. The displacements from equilibrium along the line of the springs are described by coordinates xA and xn, as shown. If either of the masses is clamped, the period T(=2 π/ ω) for one complete vibration of the other is 3 sec. (a) If both masses are free, what are the periods of the two normal modes of the system? Sketch graphs of xA and xB versus t in each mode
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