In the previous pendulum lab,
we built a pendulum, saw how it worked, learned how to make important
measurements, and then figured out what determines the period of a pendulum.
We figured it out inductively because you looked for a pattern without
following a specific experimental procedure.
No matter how, somebody could refute that finding and say you did not test
all possibilities carefully.
This investigation is heavily based on understanding how variables work in a scientific experiment.
Before you start, you should review independent variables,
dependent variables, and controlled variables.
Getting Started
First, simply rebuild the pendulum and review how to set and measure
length, mass, amplitude, and period.
Throughout this investigation, we will call length, mass, and amplitude,
the input variables, because you directly control them,
and we will call period the output variable,
because it is determined based on the input variable.
Defining a "Deductive Experiment"

A single deductive experiment consists of a single independent variable,
a single dependent variable,
and as many controlled variables as necessary.

The experimenter systematically sets the independent variable to a series
of different values.

For each value of the independent variable,
the experimenter measures the value of the dependent variable.

While changing the independent variable,
each controlled variable is set to a constant value and never changed.
This ensures that, if there is a change in the dependent variable,
it comes from the changes in the independent variable and no other factor.

Based on the results, the experimenter determines if there is a
causal relationship between the independent and dependent variables.
The Task
The task here is to conduct three separate
deductive experiments using the pendulum.
Each experiment must meet the following requirements.

For each experiment, select on of the three input variables (length, mass, or amplitude) as your independent variable.

For each experiment, the period must be the dependent variable.

For each experiment, the two input variables that are not your independent variable must be controlled.

You must have six different measurements for each independent variable,
and for each one a corresponding measurement of the dependent variable.

For each experiment, the greatest value of the independent variable
must be at least four times the lowest value.
This is to ensure that these is sufficient variability,
so that if there is a change in the dependent variable, it will be observed.
[Note: if your lab is already completed with 3x, you do not need to redo the lab.]

Do not pick values of amplitude greater than 45 degrees.

The values of the independent variable do not need
to be in regular increments, though they may be.
For example, they do not need to be 10, 15, 25, 30...
they could be 12, 19, 23, 28...
Don't do this!!!
The most common error is mistaking an experiment
with a measurement.
A single experiment must consist of several measurements.
This complete investigation consists of three separate experiments,
each with at least 6 measurements,
for a total of 18 measurements.
LAB REPORT FORMAT
Formatting of assignments is crucial because the format should reflect the goal of the assignment.
In this assignment, the goal was to design experiments.
Therefore, the formatting needs to reflect proper experimental design
3 Sections, Each Describing an Experiment
Your report should be broken into three different sections,
each describing one of the three experiments you conducted.
Each experiment must be presented as an independent unit,
separate from the others.
The writeup of each experiment should be as though you didn't even do the other two.
Requirements for Each Experiment Writeup

Definitions of Variables:
In this section, you define the variables for your experiment.

Define the independent variable: (mass, length, or amplitude)

Define the dependent variable: (period)

Define the two controlled variables (mass, length, or amplitude),
and write the constant value of each of those controlled variables.
"Definitions of variables" does not mean that you are writing the
dictionary definition of independent, dependent, and controlled variables,
but that you are showing what variables you defined as independent, dependent and controlled.
This section does not need to be longer than a short list.

Data Table:
In this section, you will write each value chosen for the independent variable (on the left),
and a corresponding measurement for the dependent variable (on the right).
Make sure to properly label your table and include units in the headers.
The rows of the table should be ordered in increasing values of the independent variable.

Scatter Plot:
In this section, you draw a handwritten** scatter plot.
The independent variable should be on the horizontal axis
and the dependent variable should be on the vertical axis.
In the scatter plot, do not connect points or add a best fit line,
only show each point. (You are not adding your own analysis, only relevant data).

Analysis:
In this section, you answer a few questions about the relationship
between the independent and dependent variables.
For full credit, you must use the terms
"independent variable" and "dependent variable"
correctly in this analysis section.
However, the analysis does not need to be more than a few sentences long!

Do the data suggest there is a relationship
between the independent and dependent variable?

If #1 is yes, does this relationship appear to be positive or negative? (if #1 is no, your analysis is complete)

In a positive relationship, an increase in the independent variable
is associate with an in in the dependent variable.

In a negative relationship, an increase in the independent variable
is associated with a decrease in the dependent variable.

If #1 is yes, does this relationship appear to be linear or nonlinear?

In a linear relationship, any change of one unit
in the independent variable is associated with a regular change
of some number of units in the dependent variable.

In a nonlinear relationship, any change of one unit
in independent variable can be associated with different changes
in the dependent variable.

Linear relationships can be identified on a scatter plot:
if the points are not in a straight line, then the relationship
is probably probably nonlinear.
**I prefer handwritten graphs because I think the process of plotting each point
helps you think more clearly about what the points mean.
This manual process is lost when a computer creates your graph in an instant.
Example:
Experiment 1

Definitions of variables:

Independent Variable: ____________________

Dependent Variable: ____________________

Controlled Variables and Values: ____________________

Data Table:

Scatter Plot:

Analysis:
Experiment 2

Definitions of variables:

Independent Variable: ____________________

Dependent Variable: ____________________

Controlled Variables and Values: ____________________

Data Table:

Scatter Plot:

Analysis:
Experiment 3

Definitions of variables:

Independent Variable: ____________________

Dependent Variable: ____________________

Controlled Variables and Values: ____________________

Data Table:

Scatter Plot:

Analysis:
Remember that the key to having a good science report is not a long report,
but a concise report that clearly organizes information!