A pendulum of length with a bob of mass *m* is oscillating with small amplitude. Which of the following changes in the pendulum would double its period?

### Select an Answer

Doubling the mass *m* of the bob

Doubling the initial force used to set the pendulum in motion

Doubling the amplitude of the pendulum’s swing

Quadrupling the mass *m* of the bob

Quadrupling the length $\ell $ of the pendulum

### View Correct Answer

The correct answer is quadrupling the length of the pendulum. The period of a pendulum is directly proportional to the square root of its length. Thus if the length of the pendulum is increased by a factor of , its period will be increased by a factor of . The period is independent of the mass of the bob, and for small oscillations it is independent of the amplitude and hence also of the force required to set it in motion.