Question

part a

a simple pendulum consists of a point mass suspended by a weightless, rigid wire in a uniform gravitation field. which of the following statements are true when the system undergoes small oscillations? check all that apply.

• the period is proportional to the length of the wire.
• the period is inversely proportional to the suspended mass.
• the period is proportional to the suspended mass.
• the period is inversely proportional to the length of the wire.
• the period is independent of the length of the wire.
• the period is independent of the suspended mass.

Explanation:

State the pendulum period formula

Using the Simple Pendulum Period knowledge point

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

Analyze mass dependence

Using the Simple Pendulum Period knowledge point

$$ \frac{\partial T}{\partial m} = 0 $$

The period \(T\) is independent of the suspended mass \(m\).

Analyze length dependence

Using the Simple Pendulum Period knowledge point

$$ T \propto \sqrt{L} $$

The period \(T\) is proportional to the square root of the length \(L\), meaning it is not directly proportional to \(L\), nor inversely proportional to \(L\), nor independent of \(L\).

Answer:

• The period is proportional to the length of the wire.
• The period is inversely proportional to the suspended mass.
• The period is proportional to the suspended mass.
• The period is inversely proportional to the length of the wire.
• The period is independent of the length of the wire.
• The period is independent of the suspended mass. (Correct answer)