Problem 4. Consider the five different simple pendula (labeled A through E) shown below. The figure shows each pendula sitting in its rest position. The length and mass of each simple pendulum is given in terms of a general length L and mass m. For parts (a) and (b) of this problem, suppose that each of the five pendula are released from rest at the same angle relative to each pendulum's vertical position. B D E L 0.5L 2L L 1.5L m 2m 0.5m 2m 3m These are all simple pendula! The difference in size of each mass is not relevant. (relative to each Part (a) If all five pendula are released from rest at the same angle pendulum's vertical position), rank from first to last the order in which the five pendula will first pass through its vertical position. Support your reasoning. (relative to each Part (b) If all five pendula are released from rest at the same angle pendulum's vertical position), rank from largest to smallest the speed of each pendulum when it first passes through its vertical position. Support your reasoning. Part (c) Now, suppose that each of the five masses is attached to an identical spring with restoring constant k. Rank from largest to smallest the angular frequency of oscillation for each of the masses. Support your reasoning.
Problem 4. Consider the five different simple pendula (labeled A through E) shown below. The figure shows each pendula sitting in its rest position. The length and mass of each simple pendulum is given in terms of a general length L and mass m. For parts (a) and (b) of this problem, suppose that each of the five pendula are released from rest at the same angle relative to each pendulum's vertical position. B D E L 0.5L 2L L 1.5L m 2m 0.5m 2m 3m These are all simple pendula! The difference in size of each mass is not relevant. (relative to each Part (a) If all five pendula are released from rest at the same angle pendulum's vertical position), rank from first to last the order in which the five pendula will first pass through its vertical position. Support your reasoning. (relative to each Part (b) If all five pendula are released from rest at the same angle pendulum's vertical position), rank from largest to smallest the speed of each pendulum when it first passes through its vertical position. Support your reasoning. Part (c) Now, suppose that each of the five masses is attached to an identical spring with restoring constant k. Rank from largest to smallest the angular frequency of oscillation for each of the masses. Support your reasoning.
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Problem 4.
Consider the five different simple pendula (labeled A through E)
shown below. The figure shows each pendula sitting in its rest position. The length and mass of
each simple pendulum is given in terms of a general length L and mass m. For parts (a) and (b)
of this problem, suppose that each of the five pendula are released from rest at the same angle
relative to each pendulum's vertical position.
B
D
E
L
0.5L
2L
L
1.5L
m
2m
0.5m
2m
3m
These are all simple pendula! The difference in size of each mass is not relevant.
(relative to each
Part (a) If all five pendula are released from rest at the same angle
pendulum's vertical position), rank from first to last the order in which the five pendula
will first pass through its vertical position. Support your reasoning.
(relative to each
Part (b) If all five pendula are released from rest at the same angle
pendulum's vertical position), rank from largest to smallest the speed of each pendulum
when it first passes through its vertical position. Support your reasoning.
Part (c) Now, suppose that each of the five masses is attached to an identical spring with
restoring constant k. Rank from largest to smallest the angular frequency of oscillation
for each of the masses. Support your reasoning.
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