Professor Mattox's Pendulum Study for Astronomy Students

Your name:________________________; Points: ______(20 points extra-credit possible)

Last modified 11/14/06.

Introduction

There are two types of pendulums - the compound and the simple. A compound pendulum has its mass distributed throughout its length. A simple pendulum has its mass concentrated at a point called the bob. Although the definition of a point is a position without dimension, a pendulum is still considered to be simple if the mass of the supporting device (string) is negligible in comparison to that of the bob, and the supporting device is long in comparison to the diameter of the bob.

A pendulum demonstrates continuous transformation of energy: potential energy to kinetic energy; kinetic energy back to potential energy; potential energy back to kinetic energy; etc. It is suggested that you watch the animation on our text publisher's wesite called "Conservation of Potential and Kinetic Energy" that demonstrates this.

The figure above shows the evolution of a simple pendulum during one fourth of a period. A period is the interval of time required for the pendulum to return to the position it had at the beginning of the period with the same velocity.

Write an equation for the potential energy at the position on the right.

What is the kinetic energy at the position on the right?

What is the kinetic energy at the position shown at the left of the figure?

What is the potential energy at the position shown at the left of the figure?

Describe in three sentences what will happen during the remaining 3/4 period following the 1/4 period shown above.

In the absence of friction, how long will a pendulum continue to oscillate?

For small displacement, the period of a simple pendulum depends only upon the length of a pendulum and the acceleration of gravity. The formula is:

Equation 1: T=2*Pi*(L/g)^(1/2)

Where Pi is the constant, 3.14; T= the period; L= the length; and g= the acceleration due to gravity = 9.8 m/s^2.
How much will the period increase when the length is doubled?

Would a pendulum at the North pole oscillate faster or slower than a pendulum at the equator?

How do you expect the period to depend on the mass of the bob?

How do you expect the period to depend on the amount of displacement of the bob?

Foucault Pendulum

At the north end of the first floor of the Lyons Science Building you will find a Foucault Pendulum. What employment lead Foucault to the invention of his Pendulum?

Where did he first operate his pendulum?

When and where did he first demonstrate his pendulum to the public?

Is our Foucault Pendulum simple or compound? Why?

Is the displacement of this pendulum decaying due to loss of energy due to friction?

Explain why (or why not?)

Measure the period of our Foucault Pendulum:
Number of periods measured:__________
T for these N periods:__________
T for 1 period:__________

Use Equation 1 to calculate the expected length for this period (in m) using your value of T.

What is the actual length? Hint, read the sign.

Calculate the percentage difference between these lengths.

Discuss possible reasons for discrepancy.

The plane of oscillation of this pendulum is expected to make one complete revolution every 41.72 hours. Why does it revolve?

Verify the rate of rotation of the plane of oscillation of this pendulum. Report your procedure, data, and conclusions. Calculate the percentage difference between your determination of the period of the rotation of the plane of oscillation and the expected 41.72 hours. Discuss possible reasons for the observed discrepancy.

Demonstrate mathematically why the period of rotation of the plane of oscillation of this pendulum is expected to be 41.72 hours (and not, say, 24.00, or 23.93 hours).