To obtain Equation 3.15 we limit ourselves to small angles. What exactly qualifi
ID: 1416804 • Letter: T
Question
To obtain Equation 3.15 we limit ourselves to small angles. What exactly qualifies as a small angle? The goal of this lab is to study the motion of a pendulum to determine when the small angle approximation breaks down.
Interpret your results. What are you able to conclude from your data? Describe how your conclusions relate to the physical principles being studied.
A (amplitude) w(angulafrequ A uncerta W uncerta 3.496 Expected Trail 1 Trail 2 Trail 3 Trail4 Trail 5 Trail 6 3.2 0001472 0000564 3.487 0000646 0.002297 3.418 0,0008380,000864 349 0.000643 0L009535 3.447 0000747 0,001034 3.479 0.000749 0.00241 Trail 700006293.493 0000629 0.006558 1.156 0.1346 5105 003312 04406 0.2214Explanation / Answer
in the given data,
From trail 2 to trail 7 - If the amplitude of the pendulum is increased, the angular frequency of the simple harmonic motion is decreased.
this is because of damping in the SHM.
Damping & Damping Coefficient:
When a damped oscillator is subject to a damping force which is linearly dependent upon the velocity, such as viscous damping, the oscillation will have exponential decay terms which depend upon a damping coefficient. If the damping force is of the form
Fdamping=-cv
i.e. Fdamping is directly proportional to the velocity of the simple pendulum
From the above explanation and the given data,
as the amplitude of the pendulum motion increases, the maximum velocity of the mass at also increases.
Damping & Damping Coefficient:
When a damped oscillator is subject to a damping force which is linearly dependent upon the velocity, such as viscous damping, the oscillation will have exponential decay terms which depend upon a damping coefficient. If the damping force is of the form
Fdamping=-cv
i.e. Fdamping is directly proportional to the velocity of the simple pendulum
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