Time swinging The period T time in seconds for one complete

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

Solution

8T^2 = (pi)^2 L
Given L = 10 feet
Plugging in this value in the above equation..
8T^2 = (pi)^2(10)
8T^2/8 = (pi)^2(10)/8
==> t^2 = (pi)^2(5/4)
Taking square root on both the sides..
T = Sqrt[(pi)^2(5/4)]
==> T = (Pi/2)sqrt(5)
==> T = (3.14/2)(2.236)
==> T = 3.5
The time taken by the child to complete one cycle = 3.5 seconds.