# Frostbite Theater

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

Two pendulums are made using washers and string. One pendulum is made using one washer while the other is made using four. Other than that, the pendulums are as identical as we can make them. If they are displaced by the same amount, which will be the first to complete ten swings?

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: Two pendulums are made using washers and string.

Joanna: One is made with one washer while the other's made with four.

Steve: Other than that, the pendulums are as identical as we can make them.

Joanna: Each pendulum is made with the same length of string, displaced by the same amount, and allowed to swing freely.

Steve: Which pendulum will be the first to complete ten swings?

Joanna: Will it be the one with one washer?

Steve: Will it be the one with four washers?

Joanna: Will it be a tie?

Steve: Or, will they not be able to complete ten swings?

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

Steve: If the angular displacement is small, the amount of time it takes for a simple pendulum to complete one swing is given by two pi times the square root of the quantity 'L' divided by 'g', where 'L' is the effective length of the pendulum and 'g' is the acceleration due to gravity.

Joanna: So why doesn't the mass matter? While the set of four washers experiences four times the gravitational force as the single washer, they also have four times the inertia. So, both sets of washers undergo the same acceleration.

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

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