Which of the following statements about the motion of a simple pendulum is true?

Analyze the question: We need to find the one true statement about a simple pendulum.

Key concepts:

• Period of a simple pendulum: T = 2π√(L/g)
• SHM only occurs for small angles (below about 10°), because only then sin θ ≈ θ.
• At the equilibrium (lowest) point, the speed is maximum and the kinetic energy is maximum.
• At the extreme positions, the speed is zero, the kinetic energy is zero, and the potential energy is maximum.

Check each option:

• A. SHM when the angle is large: False. SHM requires small angles. For large angles the restoring force is not proportional to displacement.
• B. Passes equilibrium with minimum speed: False. Speed is maximum at the equilibrium position.
• C. Maximum kinetic energy at extreme positions: False. At the extremes the bob momentarily stops, so KE = 0 and PE is maximum.
• D. Swings faster at the poles than at the equator: Consider g. It is larger at the poles (about 9.83 m/s²) than at the equator (about 9.78 m/s²), because the Earth is slightly flattened and also because of the Earth's rotation. Since T = 2π√(L/g), a larger g gives a smaller period, so the pendulum completes each swing in less time. It therefore swings faster (higher frequency) at the poles. True.

Answer: D

Tip: Remember "big g, short T." Anything that increases g (like going to the poles or to sea level) makes a pendulum oscillate faster. Also remember that for a pendulum, KE is maximum at the bottom, and PE is maximum at the ends.