a pendulum initially swings through an arc that is 20 inches long. on each swing, the length of the arc is 0.85 of the previous swing.
a) write a recursive model of geometric decay to represent the sequence of lengths of the arc of each swing. let p1=20
b) rewrite your model from part (a) using an explicit formula
c) what is the total distance, approximately, that the pendulum has swung when it stops?
can you also teach me how to write a recursive model properly?
I will give this a go!
P(1) =20, P(2)=20*0.85 =17, P(3) =17*0.85=14.45, P(4) =14.45*0.85 =12.2825.....and so on.
Decay =20 * 0.85^n, where n =number of swings. Example: After 10 swings, you will have:
D =20 * 0.85^10 =20 * 0.19687440434072265625=~3.94 inches from the original of 20 inches.
You can use the infinite geometric series formula to sum them up:
Sum = F / [1 -R], where F=First term, R= Common Ratio.
Sum =20 / [1 - .85]
=20 / 0.15
=133 1/3 inches - total distance of the pendulum swings.