Problem:
The length of the arc formed by the first swing of the bob of a pendulum is 20 cm. If each succeeding swing is 3/4 of the preceding one,
a. how far will it travel in the first six swings?
b. how far will it travel before it comes to rest?
Solution:
a1 = 20 cm
a2 = 20(3/4) = 15 cm
a3 = 15(3/4) = 11.25 cm
a4 = 11.25(3/4) = 8.4375 cm
a5 = 8.4375(3/4) = 6.328125 cm
a6 = 6.328125(3/4) = 4.74609375 cm
a. how far will it travel in the first six swings?
Sum = 20 + 15 + 11.25 + 8.4375 + 6.328125 + 4.74609375
Sum = 65.76171875 cm
It will travel up to 65.76171875 cm in the first six swings
b. how far will it travel before it comes to rest?
[tex]\[\begin{array}{l}S = \frac{{{a_1}}}{{1 - r}}\\\\S = \frac{{20}}{{1 - (\frac{3}{4})}}\\\\S = \frac{{20}}{{\frac{1}{4}}}\\\\S = 20(4)\\\\S = 80\end{array}\][/tex]
It will travel up to 80 cm before it comes to rest
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