440 Oscillatory MotionQ15.7We assume that the coils of the spring do not hit one another. The frequency will be higher than fbythe factor 2 . When the spring with two blocks is set into oscillation in space, the coil in the centerof the spring does not move. We can imagine clamping the center coil in place without affecting themotion. We can effectively duplicate the motion of each individual block in space by hanging asingle block on a half-spring here on Earth. The half-spring with its center coil clamped—or its otherhalf cut off—has twice the spring constant as the original uncut spring, because an applied force ofthe same size would produce only one-half the extension distance. Thus the oscillation frequency inspace is 122212πFHGIKJFHGIKJ=kmf. The absence of a force required to support the vibrating system inorbital free fall has no effect on the frequency of its vibration.
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