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Radial forcing and Edgar Allan Poe's lengthening pendulum
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10.1119/1.4816241
/content/aapt/journal/ajp/81/9/10.1119/1.4816241
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/9/10.1119/1.4816241
View: Figures

Figures

Image of Fig. 1.
Fig. 1.

Definitions of the inertial coordinate system and the noninertial coordinate system with origin at the pendulum's tip.

Image of Fig. 2.
Fig. 2.

Trajectory of a lengthening pendulum where , with in meters and in seconds. Note both the lengthening and the decreasing angular amplitude.

Image of Fig. 3.
Fig. 3.

Displacement angle vs. time for the trajectory depicted in Fig. 2 .

Image of Fig. 4.
Fig. 4.

Trajectory of a lengthening pendulum over an extended period.

Image of Fig. 5.
Fig. 5.

Depiction of the pendulum being pulled in at the bottom and let out at the high point of its cycle.

Image of Fig. 6.
Fig. 6.

Plot of pendulum state variables over one oscillation period. The positions at which pulling-in and letting-out impulses are applied are displayed. In the top panel, the units of θ are such that at the low point and at either high point of the swing.

Image of Fig. 7.
Fig. 7.

Comparison of the trajectories for different pulling and letting times, again using the convention where at the low point and at either high point of the swing. Pulling near the bottom (0.05) and letting near the top (0.95) can strongly increase the amplitude.

Image of Fig. 8.
Fig. 8.

(Color online) Normalized energy after 300 s as a function of pulling-in and letting-out impulse positions. Note the strong peak when pulling at the bottom and letting at the high points of each cycle.

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/content/aapt/journal/ajp/81/9/10.1119/1.4816241
2013-09-01
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Radial forcing and Edgar Allan Poe's lengthening pendulum
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/9/10.1119/1.4816241
10.1119/1.4816241
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