Lesson 5

Explore

Over 500 years ago, Galileo discovered that a swinging pendulum kept the same time, whether the pendulum swung in a tiny arc or in a slightly greater arc. Galileo used this understanding to measure the pulse of medical patients. He found that the length of the pendulum was the determining factor in the pendulum’s period of motion.

In Try This 2 you will model the pendulum using a radical equation.

Try This 2

Pendulum clocks can be adjusted to be accurate timekeepers by carefully adjusting the length of the pendulum.

One of the relationships of physics is that the time for a complete back-and-forth swing of a pendulum is

• directly proportional to the square root of the length

• inversely proportional to the square root of the acceleration due to gravity

The constant of proportionality is 2π.

Another way of describing the relationship is as follows:

• The time period is 2π times the square root of length divided by the square root of the acceleration due to gravity.

1. Use Write an Equation to express the relationship between the period T of a pendulum and its length. Use L for length and g for the acceleration due to gravity.
   
   
    
   
   
   
2. A pendulum in a wall clock has a length of 1.4 m. What is the time period of that pendulum to the nearest hundredth of a second if the acceleration due to gravity is 9.81 m/s2 at that location? Use Time Period of the Pendulum to find the answer.
   
   
    
   
   
   
3. Rearrange the equation in Isolate L.
   
   
    
   
   
   
4. Find the length of a pendulum that will give a time period of exactly 2 s, so that the clock will tick precisely every second as the pendulum swings back and forth. Record your answer to the nearest hundredth of a second. Use Length of a Pendulum.