I tie a spring to my back and I anchor it to the wall and see how much the spring stretches before the two forces balance.

我把弹簧一端系在背后,另一端固定在墙上,观察两个力平衡时弹簧的伸长量

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I move a little closer and I find the stretching is a different number.

我继续靠近讲台,发现弹簧伸长量有所变化

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So multiplying a vector by a number means stretch it by that factor.

所以用数字乘以矢量,就相当于将它伸长了相应的倍数

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The force may taper off, the force may not be given by a straight line, but for modest deformations, every spring will have a linear regime in which the force is linearly proportional to the stretching.

它产生的力可能会渐渐消失,力的曲线可能不是一条直线,而有轻微的弯曲,每个弹簧都有一个线性区间,在这一区间内,力和伸长量是线性关系

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We know that because you can stretch i by whatever factor you like.

因为你可以让 i 伸长任意的倍数

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It also tells you that if you compress the spring, compress it means x is now-- x is measured from this position, where the spring is neither compressed nor expanded.

它还能告诉你,如果压缩弹簧,压缩就意味着现在 x...,x 是从这个位置开始算的,在这个位置弹簧既没有压缩也没有伸长

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