Question

Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of the pendulum has an arc length of 100cm and a return swing of 99cm.

a.)On which swing will the length first have a length less than 50 cm?

b.)Find the total distance traveled by the pendulum until it comes to rest.

Answer 1

Since the nth swing has length

100*0.99^(n-1), you want to find n when

100 * 0.99^(n-1) < 50
.99^(n-1) < .5
(n-1) log.99 < log.5
n > 69.9

So, on the 70th swing the arc is less than 50 cm.

Now you know the parameters for the geometric sequence. Just use the sum formula to add up 70 terms