To obtain Equation 315 we limit ourselves to small angles Wh

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.

What does it mean experimentally for the small angle approximation to be valid? That is, what will we observe if the small angle is valid? What will be observed if the approximation is invalid?

Based on the model, what is the predicted angular frequency (or equivalently the period) for your pendulum? What is the associated uncertainty? What factors contribute most to the uncertainty? What can be done to minimize the uncertainty?

• We see from Equation 3.14 that the predicted angular frequency (or equivalently the period) does not depend on the amplitude, ?max. Is this true of the physical system as well? What will you measure to determine your answer? Based on your measurements, what happens to the angular frequency with increased amplitude? Present your data in a plot to communicate the relationship between the quantities you measured

. • Based on your data, when does the small angle approximation fail? That is, at what opening angle is the measured motion of the pendulum experimentally distinguishable from the prediction of the model?

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 0.2214

Solution

It will be easier to answer if equations are provided.

However, from the basic pronciples of pendulum motion,

Small angle appriximation yeilds a constant angular velocity. However when small angle approximation is not valid, angular momentum varry with displacement. As angle increases angular velocity decreases.

If equations are provided it will be easier answer part by part.