Station 2
Pendulum Action
Rube Goldberg Machine Design Contest Teacher Training Program
January 29, 2005
Introduction
Pendulums are found everywhere, in a grandfather clock, in a hypnotist’s office, in your
classroom, etc. There are some common misconceptions about pendulums, so at this station you
will be performing experiments that will help reveal some physical and scientific truths about
pendulums.
Background
A pendulum is simply an object that is suspended from a fixed support so that it swings freely
under the influence of gravity. The most common pendulum setup seen in physics problems is a
ball (or some other object) tied to a frictionless, massless, stretch-free string that is allowed to
swing freely from a fixed point. Other less common physics-book examples include a pendulum
clock, a spatula swinging from its end, etc.
There are two types of pendulums that we will focus on. One is called a simple pendulum; its
connecting rod (string) has very little mass compared to the object that is hanging from it. The
period of oscillation of such a simple pendulum can be approximated as
T
L
g
where T is the period of oscillation, L is the length of the connecting rod (string), and g is the
gravitational acceleration constant, which is 9.8m/s2 in metric units and 32ft/sec2 in English
units. A period is defined as one full back-and-forth swing of the pendulum bob (the object that’s
hanging from the connecting rod). The units for period, T, is seconds.
The frequency of the pendulum, or how many back and forth swings the pendulum makes in one
second, is the inverse of the period:
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f 
1

T
g
L
where f is frequency of oscillation, T is period of oscillation, g is the gravitational acceleration
constant, and L is the length of the connecting rod.
Note that the period and frequency of a simple pendulum is independent of mass. Thus to change
the oscillation period or frequency, you need to change the length of the connecting rod (since
gravity won’t change).
However, if you’re dealing with a non-simple pendulum, meaning the connecting rod is not
massless compared to the bob, not stretch-free, or induces a significant amount of friction, then
the equations become much more complicated and the mass of the bob does affect the oscillation
period and frequency. This is called a “physical pendulum.”
Experiment Time!
Purpose
Pendulums are very common in machines, especially in Rube Goldberg-like machines. It is
important that you understand the pendulum characteristics so you can maximize your resources,
keep within the time constraints of the contest, and build the best predictable pendulum. So in
this experiment, you will determine pendulum time characteristics by varying the mass of the
bob, the swing angle, the length of the connecting rod, and the mass of the connecting rod.
Procedure
Section A
1. Familiarize yourself with the stopwatch.
2. Record the mass of the bob.
3. Hold the pendulum at about 15º from the vertical.
4. Start timing as soon as the person lets go of the pendulum.
5. Stop the timer after 10 full back-and-forth oscillations and record the average time.
6. Divide the time by 10 to obtain the period of oscillation. Invert to obtain the frequency of
oscillation. Record in the table.
7. Make a prediction about the oscillation period and frequency as the mass changes
(higher, lower, same). Record in the table.
8. Repeat steps 2-7 for each mass. What did you notice about the relationship between mass,
period, and frequency?
Mass
Period?
Freq. ?
higher
lower
same
higher
lower
same
Time
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Period
Frequency
higher
lower
same
higher
lower
same
higher
lower
same
higher
lower
same
higher
lower
same
higher
lower
same
Section B
1. Place 3 fishing weights in the basket.
2. Hold the pendulum at 5º from the vertical and record the time for 10 oscillations.
3. Divide time by 10 to obtain period, and invert that value to obtain frequency.
4. Make a prediction about how the angle will affect the oscillation period and frequency for
the next angle measure.
5. Repeat the experiment for 20º, 45º, and 75º. What is the relationship between angle from
vertical and oscillation period and frequency?
Angle
Period?
Freq.?
20 degrees
higher
lower
same
higher
lower
same
45 degrees
higher
lower
same
higher
lower
same
75 degrees
higher
lower
same
higher
lower
same
Time
Period
Frequency
5 degrees
Section C
1. Place 3 fishing weights in the basket.
2. Record the length of the connecting rod (string).
3. Hold the pendulum at 15º from the vertical and record the time for 10 oscillations.
4. Divide by 10 to obtain period, and invert to obtain frequency.
5. Make a prediction about how the length of the connecting rod will affect the period and
frequency for the new length of connecting rod.
6. Repeat the experiment for 2 different lengths of string. What is the relationship between
connecting rod length and oscillation period and frequency?
Length
Period?
Freq.?
higher
lower
same
higher
lower
same
Time
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Period
Frequency
higher
lower
same
higher
lower
same
Section D
1. Replace the fishing weights with a spatula or wire whisk.
2. Hold the pendulum at 15º from the vertical and record the time for 10 oscillations. Divide
by 10 to obtain the period and invert to obtain frequency.
3. Attach 3 fishing weights to the bottom of the pendulum and record the time for 10
oscillations. What happens?
Mass
spatula or
wisk
weights
attached
Time
Period
Frequency
If there is time, you can request more objects for practice. Please ask your Station Leader.
Congratulations! Now you can design your best pendulum!
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