# A simple pendulum consists of a small mass suspended from a string that is fixed

A simple pendulum consists of a small mass suspended from a string that is fixed at its upper end and has negligible mass. The length of time, t seconds, for a complete swing of a simple pendulum can be modeled by the equation t = 2π√(L/32), where L is the length, in feet, of the string. If the time required for a complete swing of Pendulum 1 is triple the time required for a complete swing of Pendulum 2, the length of Pendulum 1's string is how many times the length of Pendulum 2's string?

1. 1/3
2. 3
3. 6
4. 9
5. 27

Let L1 feet be the length of Pendulum 1 and t1 seconds be the time for a complete swing of Pendulum 1. Let L2 and t2 describe Pendulum 2 in the same way.

The time for a complete swing of Pendulum 1 is triple the time required for a complete swing of Pendulum 2.

t1 = 3t2

As per given equation, t ∝ √L

t2 ∝ L

(t1)2 = (3t2)2

L1 = 9L2