Abstract
In this lab report, physical, torsional and simple spring pendulums and their properties were
examined. Three experimental setups were used: a mass hanging on a spring, a rod with
attached masses oscillating
...
Abstract
In this lab report, physical, torsional and simple spring pendulums and their properties were
examined. Three experimental setups were used: a mass hanging on a spring, a rod with
attached masses oscillating vertically and a rod with masses, then a disk oscillating
horizontally. Although experimental and theoretical values were close, experimental ones
were more precise and accurate, as its errors had small values. The obtained results
demonstrated that the spring constant k=19.8413± 0.209 N m . In part 2
I
1, experimental=0.0032198 ± 0.000021598 kg∗m2 and I1, t h eoretical=0.003687 ± 0.000451 kg∗m2 for
the first configuration and I2, exp=0.0041316 ± 0.000031869 kg∗m2 and
I
2, t h=0.004361 ± 0.000836 kg∗m2 for the second configuration. In the third part torsion
constant was k1=0.00943± 0.000436 kg∗m2
s
2 for the first configuration and
k2=0.008353± 0.00215 kg∗m2
s
2 for the second one. Despite of presence of errors, results
obtained in this lab were consistent. Possible sources of errors were mentioned and
discussed.
Introduction
Pendulums were in use since the 1st century, when a Chinese scientist Zhang Heng
invented seismometer. After that many inventions such as pendulum clock were
constructed and used in daily life for different purposes as time, gravity, atmospheric
pressure measurement. The first who studied pendulums and their properties was Galileo
Galilei.(3)
In this lab oscillation systems, such as simple, physical and torsional pendulums were
examined.
Simple spring pendulum was used in the first part of the experiment. It’s restoring force is
equal to the multiplication of a negative spring constant and displacement.
F
R=−kx
From this equation, a formula for the oscillation period can be derived. This gives us the
following relation, where m is the mass hanging on a spring and x is a spring constant.(2)
T=2π√mx
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