Time to Swing?

Question

The period T (time in seconds for one complete cycle) os a simple pendulum is related to the length. L (in feet) of the pendulum by the formula 8T^2 = n^2L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing?

Answer 1

You may also use the solution T = 2*pi*sqrt(L/g)

8T^2 = n^2L.

T = sqrt(n^2L/8) = sqrt(10/8) = sqrt(5/4) =sqrt(5)/2

or

T = 2*pi*sqrt(10/32.2)

Answer 2

Pendulum period in seconds

T ≈ 2π√(L/G)

L is length of pendulum in meters

G is gravitational acceleration = 9.8 m/s²

10' = 3.05 m

T = 2π√(L/G)

T = 2π√(3.05/9.8) = 3.5 seconds

I didn't use your formula as it didn't make sense. What is n?