Summary of Graphical Analysis Experiences

A complete description of the process of experimental design and analysis for investigating a relationship between variables is described in the guide, Design and Execution of a Relationship Experiment.

Chronology ID Type Name Dependent
Variable		 Independent
Variable		 Re-expression Type of fit Comparison of Theory to Fit Expected slope, m Expected intercept, b
1 G1-3c Guide Graphical Analysis for a Linear Relationship Circumference, C Diameter, D none linear
Theory: C = π D + 0
Fit: m b
π Circumference when
the diameter is 0
2 L103 Lab Measuring the Speed of Sound Distance, d Elapsed time, t none linear
Theory: d = vsound t + 0
Fit: m b
vsound Distance traveled
in 0 elapsed time
3 G1-3d Guide Graphical Analysis for a Non-Linear Relationship Area, A Diameter, D D2 linear
Theory: A = π/4 D2 + 0
Fit: m b
π/4 Area of cross section
when diameter is 0
4 L105C Lab The Simple Pendulum Period, T Length, L L0.5 linear
Theory: T = 2π(1/g)0.5 L0.5 + 0
Fit: m b
2π(1/g)0.5 = 2.01 s/m0.5 Period when length
of the pendulum is 0
5 L109 Lab Finding Acceleration by the Finite Difference Method Average velocity, vav Elapsed time, t none linear
Theory: v* = a t + vo
Fit: vav m b

*The key theoretical point of the lab is used to argue that
vav over the time interval is equal to v at the midpoint
of the time interval. Theoretically, then, we expect vav = v.

a = gsinθ,
where θ is the angle of
inclination of the
plane from the
horizontal

Initial velocity
vo
6   Prob Practice test 1 Volume, V Diameter, D D3 linear
Theory: V = π/6 D3 + 0
Fit: m b

π/6

 Volume when
diameter is 0
7   Test

Test 1, Problem 4

 Vertical position, x Elapsed time, t t2 linear
Theory: x = a/2 t2 + xo
Fit: m b
a/2 = 4.90 m/s2

Initial position,
xo
8 L115 Lab Range of a Projectile Range, x Initial horizontal velocity, vox none linear
Theory: x = t vox + xo
Fit: m b
The time of fall, t = (2y/g)0.5,
where y is the vertical
distance of fall.		 Initial horizontal
position, xo
9 L123 Lab Hooke's Law and a Measurement of Spring Constant Position, x Weight, W none linear
Theory: x = -1/k W + xo
Fit: m b
-1/k, where k
is the spring constant		 the position, xo, with no
weight hanging from
the spring

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