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Carl Witthoft
Carl Witthoft
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The risk of an "intuitive" answer is that people's intuitions often go awry.

Here's an intuitive answer: Take two identical pendulums. Release one at $\theta$ and the other at $2*\theta*$2*\theta$ from vertical. No matter what else, the pendulum that starts from farther away can never "catch up" to the other one. In addition, since it's obvious that it will have greater K.E. at vertical, it will travel farther "up" the far side. After all, if you drop two balls from different heights, the higher one will always take longer to reach the ground. (except now you need to prove that, too :-( )

That's great, but someone else will say "but what if the $2*\theta$ pendulum accelerates so fast it catches up?" [sort of like the infamous "hot water freezes faster than cold" argument] And so on. At some point you're going to have to use a little math to prove your case.

The risk of an "intuitive" answer is that people's intuitions often go awry.

Here's an intuitive answer: Take two identical pendulums. Release one at $\theta$ and the other at $2*\theta* from vertical. No matter what else, the pendulum that starts from farther away can never "catch up" to the other one. In addition, since it's obvious that it will have greater K.E. at vertical, it will travel farther "up" the far side. After all, if you drop two balls from different heights, the higher one will always take longer to reach the ground. (except now you need to prove that, too :-( )

That's great, but someone else will say "but what if the $2*\theta$ pendulum accelerates so fast it catches up?" [sort of like the infamous "hot water freezes faster than cold" argument] And so on. At some point you're going to have to use a little math to prove your case.

The risk of an "intuitive" answer is that people's intuitions often go awry.

Here's an intuitive answer: Take two identical pendulums. Release one at $\theta$ and the other at $2*\theta$ from vertical. No matter what else, the pendulum that starts from farther away can never "catch up" to the other one. In addition, since it's obvious that it will have greater K.E. at vertical, it will travel farther "up" the far side. After all, if you drop two balls from different heights, the higher one will always take longer to reach the ground. (except now you need to prove that, too :-( )

That's great, but someone else will say "but what if the $2*\theta$ pendulum accelerates so fast it catches up?" [sort of like the infamous "hot water freezes faster than cold" argument] And so on. At some point you're going to have to use a little math to prove your case.

Source Link
Carl Witthoft
Carl Witthoft
  • 11.1k
  • 2
  • 20
  • 30

The risk of an "intuitive" answer is that people's intuitions often go awry.

Here's an intuitive answer: Take two identical pendulums. Release one at $\theta$ and the other at $2*\theta* from vertical. No matter what else, the pendulum that starts from farther away can never "catch up" to the other one. In addition, since it's obvious that it will have greater K.E. at vertical, it will travel farther "up" the far side. After all, if you drop two balls from different heights, the higher one will always take longer to reach the ground. (except now you need to prove that, too :-( )

That's great, but someone else will say "but what if the $2*\theta$ pendulum accelerates so fast it catches up?" [sort of like the infamous "hot water freezes faster than cold" argument] And so on. At some point you're going to have to use a little math to prove your case.