a Pendulum Travels β a Pendulum Swings

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.

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.