# Frostbite Theater

Here's a Question! - Swinging Pendulums (Different Angles)

A pendulum is made using washers and string. The pendulum is displaced from its resting position and is allowed to swing freely. Later, the pendulum is displaced by a smaller amount and is again allowed to swing freely. Which set-up will complete ten swings first?

Announcer: Frostbite Theater presents... Cold Cuts! No baloney!

Joanna and Steve: Just science!

Joanna: Hi! I'm Joanna!

Steve: And I'm Steve!

Joanna: Here's a question for you...

Steve: A pendulum is made out of some washers and string.

Joanna: The pendulum is displaced from its resting position and is allowed to swing freely.

Steve: Later on, this is repeated with the same pendulum, but using a smaller displacement.

Joanna: Which set-up will complete ten swings first?

Will it be the one with the large displacement?

Steve: Will it be the one with small displacement?

Joanna: Will it be a tie?

Steve: Or, will one, or both of them, stop before they swing ten times?

Joanna: Pause the video now if you'd like to think it over before we show you what happens.

Steve: Now, someone out there is probably saying "Wait, wait, wait, wait wait... The period of a simple pendulum is given by two pi times the squareroot of L divided by g. The angle of displacement has nothing to do with it."

Joanna: But, that equation is an approximation. If you remember, it's derived by replacing the sine of an angle with the measure of an angle, which is reasonable as long as the angle is small and measured in radians. It's still an approximation, though. And, the larger the displacement, the less accurate it is.

Thanks for watching. I hope you'll join us again soon for another question!

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