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 a1=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 a1=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 a1=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
