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Physics 4AL
Lab for Science and Engineering Mechanics
Experiment 5:
Simple and Damped Harmonic Motion
Lab Section:
LAB 5
Name:
SunYi Lim
UID:
503576474
Date:
7/20/10
TA:
Chris Tyndall
Partner:
Jaimie Yap
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The purpose of this experiment is to analyze a simple spring system and verify relationships such as Hook’s
Law, simple harmonic motion, and damped harmonic motion. The setup consists of a spring, mass, string, and force
transducer. The force transducer is used to make an indirect measurement of the position of the mass as a function of
time. After the value of the spring constant is found though Hooke’s Law, the period of oscillation and relative peak
to peak amplitudes will be analyzed. Hooke’s Law states that:
=
F
kx
We will calculate the period, amplitude, and frequency of both simple harmonic motion and damped harmonic
motion. We will also calculate Q, or the quality factor, of damped harmonic motion.
Using the basic equation from the Hooke’s Law, which states that:
= 
F
kx
Where
F
is force (N),
x
being the displacement (in meters) and
k
, which is the spring constant. The spring constant
is obtained by plotting force vs. displacement graph. Regression is performed to determine the slope (the spring
constant) and the uncertainty.
Once the appropriate voltage is obtained using the transducer and the spring, we will measure at least five
oscillations to calculate the amplitude:
=
+ 
An Vn 1 Vn
Where
A
is amplitude,
+
Vn 1
is the local maximum voltage, and
Vn
is the local minimum voltage.
Using the amplitude calculated, the amplitude ratio (
Rn
) will be calculated to find the quality of each type
of the motion:
=
+
Rn An 1An
At least 5 R’s should be calculated to obtain a good average value for Q.
Each Q can be calculated and averaged out in following fashion:
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This note was uploaded on 07/21/2010 for the course PHYSICS 4A Physics taught by Professor Slater during the Summer '10 term at UCLA.
 Summer '10
 SLATER

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