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438_Physics ProblemsTechnical Physics

438_Physics ProblemsTechnical Physics - 440 Q15.7...

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440 Oscillatory Motion Q15.7 We assume that the coils of the spring do not hit one another. The frequency will be higher than f by the factor 2 . When the spring with two blocks is set into oscillation in space, the coil in the center of the spring does not move. We can imagine clamping the center coil in place without affecting the motion. We can effectively duplicate the motion of each individual block in space by hanging a single block on a half-spring here on Earth. The half-spring with its center coil clamped—or its other half cut off—has twice the spring constant as the original uncut spring, because an applied force of the same size would produce only one-half the extension distance. Thus the oscillation frequency in space is 1 2 2 2 12 π F H G I K J F H G I K J = k m f . The absence of a force required to support the vibrating system in orbital free fall has no effect on the frequency of its vibration.
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