so that it'll go faster for most of the time, that's very clear.

使得它多数时候运动得快一些这是显然的
But the fact that it goes faster in exactly the right way

但是速度的增加使得它恰好能够
to complete the trip at the same time,

在相同的时间内完成运动
is rather a miraculous property of the fact

是一个十分奇妙的性质
that this equation has this particular form.

它来源于这个方程的特定形式
If you tamper with this, if you add to this a little bit,

如果你想破坏这一切的话如果加上这一项
like 1 over 100 times x^3, then all these bets are off.

像是 1 除以 100 乘以 x^3 那么这些全完了
It's got to be that equation for that result to be true.

结论要成立的话方程一定是那样的
Okay. So, this is simple harmonic motion.

这就是简谐运动
Then, you can do the following variant of this solution,

接下来我们可以对这个解做一些变形
which I will write down now.

我现在把它写下来
Suppose I set my clock to 0, right there.

假设我把这里作为计时起点