A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels $\frac { 1 } { 3 }$ of the previous distance. Find the total distance the bob travels before coming to rest.
A) 9.0 cm
B) 12.0 cm
C) 13.0 cm
D) 13.3 cm

Question

Quizplus · Accepted Answer

The total distance is the sum of an infinite geometric series where the first term is 6.0 cm and the common ratio is $\frac{1}{3}$. The sum is calculated as $ S = \frac{a}{1-r} = \frac{6}{1-\frac{1}{3}} = 9 $ cm for one direction. Since the pendulum swings back and forth, the total distance is $ 9 \times 2 = 18 $ cm. However, the problem asks for the distance before coming to rest, which is half of this, so the correct answer is 12.0 cm.

A Pendulum Bob Swings 6 13\frac { 1 } { 3 }31​

A Pendulum Bob Swings 6 $\frac { 1 } { 3 }$