Question

part a

you would like a pendulum that swings back and forth once every 2 seconds, but the one you have swings once every 1.9 seconds. which of the following should do to adjust it so that it has the desired period?

• remove some mass from the pendulum.
• add more mass to the pendulum.
• make the pendulum slightly longer.
• make the pendulum slightly shorter.

part b

you and a friend are on a swing set and her swing is slightly longer than yours. if you both start swinging at the same time, from the same height, where will she be after you have completed one complete swing back and forth?

• she will still be at the same height as you.
• she will be slightly lower than you but moving downward away from you.
• she will be slightly higher than you.
• she will be slightly lower than you but moving upward toward you.

Explanation:

Analyze Part A period adjustment

Using the Simple Pendulum Period knowledge point

$$ T = 2\pi \sqrt{\frac{L}{g}} $$

To increase the period \(T\) from \(1.9\text{ s}\) to \(2\text{ s}\), the length \(L\) must be increased.

Analyze Part B relative motion

Using the Simple Pendulum Period knowledge point

$$ T_{\text{friend}} > T_{\text{you}} \implies f_{\text{friend}} < f_{\text{you}} $$

When you complete one full cycle, she has not yet completed hers. Since she is lagging behind, she is still on her way back up toward the starting height, meaning she is lower than you but moving upward toward you.

Analyze Part C period independence

Using the Simple Pendulum Period knowledge point

$$ T = 2\pi \sqrt{\frac{L}{g}} $$

For small angles, the period of a simple pendulum is independent of its amplitude.

Answer:

Question 1

• Remove some mass from the pendulum.
• Add more mass to the pendulum.
• Make the pendulum slightly longer. (Correct answer)
• Make the pendulum slightly shorter.

Question 2

• She will still be at the same height as you.
• She will be slightly lower than you but moving downward away from you.
• She will be slightly higher than you.
• She will be slightly lower than you but moving upward toward you. (Correct answer)