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Question 34 of 36

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SAT Subject Test

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

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Doubling the mass m of the bob

Correct Answer: 
No

Doubling the initial force used to set the pendulum in motion

Correct Answer: 
No

Doubling the amplitude of the pendulum’s swing

Correct Answer: 
No

Quadrupling the mass m of the bob

Correct Answer: 
No

Quadrupling the length of the pendulum

Correct Answer: 
Yes

The correct answer is quadrupling the length ell 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 4, its period will be increased by a factor of 2. 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.

Question Difficulty: 
hard