ch15-p019 - 19. (a) Let x1 = FG IJ HK 2 t A cos 2 T be the...

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be the coordinate as a function of time for particle 1 and = 2 2 + 6 2 x At T cos ππ F H G I K J be the coordinate as a function of time for particle 2. Here T is the period. Note that since the range of the motion is A , the amplitudes are both A /2. The arguments of the cosine functions are in radians. Particle 1 is at one end of its path ( x 1 = A /2) when t = 0. Particle 2 is at A /2 when 2 π t / T + π /6 = 0 or t = – T /12. That is, particle 1 lags particle 2 by one- twelfth a period. We want the coordinates of the particles 0.50 s later; that is, at t = 0.50 s, 1 20 . 5 0 s =c o s =0 . 2 5 2 1.5 s A x A π × §·
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