Scientific Information About Pendulums

A simple pendulum has many uses.

The pendulum is an important device in both physics and the development of human history. Prior to the invention of the pendulum-driven clock during the Renaissance, technology had stagnated in the West. The accuracy of the new pendulum clock helped drive forward a resurgence in technology and invention that continues to this day.

History

History often records Galileo as the inventor of the pendulum because he investigated its many properties during his lifetime. However, Galileo's designs for a pendulum clock were never realized during his lifetime and the first clock to use a pendulum was built by Dutch physicist, inventor and mathematician Christian Huygens. His designs are still featured in many modern clockwork watches.

Features

At its most basic, a pendulum is a mass fixed to the end of a string and allowed to swing freely. It will oscillate in a vacuum at a set frequency that depends solely on the length of the string, meaning the size of the mass is irrelevant. This allows for clocks of varying sizes to be created using the same basic principles because they are not constrained by the size of the weight being used.

Time Frame

The complexity of the equation for determining a pendulum's period of oscillation depends on the angle through which it is displaced. If the angle is small enough that it can be reasonably equated to the sine of itself, the pendulum will display simple harmonic motion and the period is simply T = 2π x √(L/g). Here L is the length of the string and g is gravity.

Benefits

Regardless of the equation's complexity, the fact that pendulums oscillate with a clearly defined and regular period means they are exceptionally well-suited for making clocks. Furthermore, the fact that at small angles a pendulum's frequency depends solely on the length of the string and gravity means it is possible to determine the true value of acceleration due to gravity using a simple experiment involving timing a mass on a few lengths of string.

Potential

Aside from their use in clocks, pendulums have benefited engineering for centuries. Because, outside of a vacuum, movement of the pendulum is affected by air resistance, so its natural state is to hang vertically. A pendulum can therefore be used as a plumb line, which is a simple way of measuring the straightness of a vertical surface. Engineers hold the pendulum over a set point on the ground to ensure a point on a vertical surface is straight.

References

• Daniel A. Russell, Ph.D.: The Simple Pendulum
• Some Mathematical Works of the 17th and 18th Centuries: Christian Huygens: Horologium Oscillatorium