π Example1. A pendulum swings with an arc length of 24 feet on its first swing. On each swing after the first swing, the arc length is 60% of the length of the previous swing. Draw a graph that represents the arc length after each swing.

β Solution:

Make a table of values.

Swing | Arc Length |
---|---|

1 | 24 |

2 | 0.6(24)=14.4 |

3 | 0.6(14.4)=8.64 |

4 | 0.6(8.64)=5.184 |

5 | 0.6(5.184)=3.1104 |

6 | 0.6(3.1104)=1.86624 |

Graph the swing on the *x*-axis and the arc length on the y-axis.

π Ex2. A pendulum travels 12 centimeters on its first swing and 95% of that distance on each swing thereafter. Find the total distance traveled by the pendulum when it comes to rest.

β Solution:

Given *a*_{1}=12 and *r*=95% or 0.95

Find the sum.

The pendulum travels 240 cm.

Answer: 240 cm

π Ex3. The first swing of a pendulum travels 30 centimeters. If each subsequent swing travels 95% as far as the previous swing, find the total distance traveled by the pendulum after the 30th swing.

β Solution: Given *a*_{1}=30 cm, *r*=95%, *n*=30.

Find the sum.

The distance traveled is about 471 cm.

Answer: about 471 cm

π Ex4. Laurie swings a pendulum. The distance traveled per swing decreases by 15% with each swing. If the pendulum initially traveled 10 inches, find the total distance traveled when the pendulum comes to a rest.

β Solution:

Given

*a*

_{1}=10 in. and

*r*=100%-15%=0.85

Find the sum.

The distance traveled by the pendulum is about 66.7 inches.

Answer: about 66.7 inches