# 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?

- 1/3
- 3
- 6
- 9
- 27

### Answer

**The correct answer is D.**

Let L_{1} feet be the length of Pendulum 1 and t_{1} seconds be the time for a complete swing of Pendulum 1. Let L_{2} and t_{2} 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.

t_{1} = 3t_{2}

As per given equation, t ∝ √L

t^{2} ∝ L

(t_{1})2 = (3t_{2})2

L_{1} = 9L_{2}