Question

part c

two pendulums have identical periods. one has a slightly larger amplitude than the other, but both swing through small angles compared to vertical. which of the following must be true of the pendulum that has the larger amplitude?

• it is longer than the other one.
• it has more mass than the other one.
• it moves faster at the lowest point in its swing than the other one.

part d

if astronauts built a pendulum on the moon that was exactly the same as one on earth, what would be different about the pendulums motion on the moon?

• it would run slower.
• it would run faster.
• the pendulum would not run at all because things on the moon are weightless.
• there would be no difference if they were identical.

Explanation:

Analyze Part C period and length

Using the Simple Pendulum Period knowledge point

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

Since both pendulums have identical periods \(T\) and experience the same gravitational acceleration \(g\), they must have the exact same length \(L\). Mass does not affect the period.

Analyze Part C maximum speed

Using the Simple Harmonic Motion Speed knowledge point

$$ v_{\text{max}} = \omega A = \frac{2\pi}{T} A $$

Since the period \(T\) is identical for both, the pendulum with the larger amplitude \(A\) must have a larger maximum speed \(v_{\text{max}}\), which occurs at the lowest point of its swing.

Analyze Part D gravity on the Moon

Using the Simple Pendulum Period knowledge point

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

The acceleration due to gravity on the Moon \(g_{\text{Moon}}\) is smaller than that on Earth \(g_{\text{Earth}}\). Since \(g\) is in the denominator, a smaller \(g\) results in a larger period \(T\), meaning the pendulum takes more time to complete each swing and thus runs slower.

Answer:

Question 1

• It is longer than the other one.
• It has more mass than the other one.
• It moves faster at the lowest point in its swing than the other one. (Correct answer)

Question 2

• It would run slower. (Correct answer)
• It would run faster.
• The pendulum would not run at all because things on the Moon are weightless.
• There would be no difference if they were identical.