Pendulum Motion Calculations

The video tutorial explains how to calculate the time it takes for a pendulum to swing back and forth using a mathematical function. It demonstrates how to determine the swing time for a 7-foot pendulum and how to find the pendulum's length if the swing time is known. The tutorial includes step-by-step calculations and uses a calculator for decimal approximations.

What does the function s(x) = 2π√(x/32) represent in the context of pendulum motion?

• The weight of the pendulum

• The length of the pendulum

• The time for one complete swing

• The speed of the pendulum

In the function s(x) = 2π√(x/32), what does 'x' represent?

• The mass of the pendulum

• The length of the pendulum in feet

• The angle of swing

• The time in seconds

How long does it take for a 7-foot pendulum to swing back and forth once?

• 2.9 seconds

• 3.5 seconds

• 1.5 seconds

• 4.2 seconds

What is the first step in calculating the time for a 7-foot pendulum using the function?

• Square the result

• Divide by 2π

• Substitute 7 for x

• Multiply by 32

In the context of pendulum motion, what does the variable 's' represent?

• The angle of swing

• The mass of the pendulum

• The time for one swing

• The length of the pendulum

If a pendulum takes 8 seconds to swing back and forth, what is the first step to find its length?

• Multiply by 32

• Subtract 8 from the equation

• Divide by 2π

• Square the time

After isolating the square root in the equation, what is the next step to find the pendulum's length?

• Add 32 to both sides

• Square both sides

• Divide by 8

• Multiply by 2π

What is the approximate length of a pendulum that takes 8 seconds to complete one swing?

• 60.2 feet

• 51.9 feet

• 70.5 feet

• 45.3 feet

What mathematical operation is used to eliminate the square root in the pendulum length equation?

• Addition

• Subtraction

• Multiplication

• Squaring

What is the final step to find the pendulum's length after squaring both sides of the equation?

• Subtract 4 from both sides

• Divide by 2π

• Multiply by 32

• Add 8 to both sides