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3-8. A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by х— а(ф — sin ф), y = a(cos o – 1) - where the length of the pendulum is l = 4a, and where ø is the angle of rotation of the circle generating the cycloid. Show that the oscillations are exactly isochro- nous with a frequency wo = /g/l, independent of the amplitude.

3-8. A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by х— а(ф — sin ф), y = a(cos o – 1) - where the length of the pendulum is l = 4a, and where ø is the angle of rotation of the circle generating the cycloid. Show that the oscillations are exactly isochro- nous with a frequency wo = /g/l, independent of the amplitude.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The question is about analytical mechanics / classical mechanics.

3-8. A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by x = a(d sin o), y = a(cos o - 1) where the length of the pendulum is l= 4a, and where o is the angle of rotation of the circle generating the cycloid. Show that the oscillations are exactly isochro- nous with a frequency wo = Vg/1, independent of the amplitude. *The reader unfamiliar with the properties of cycloids should consult a text on analytic geometry. PROBLEMS 139 2a m FIGURE 3-A Problem 3-8.
Transcribed Image Text:3-8. A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by x = a(d sin o), y = a(cos o - 1) where the length of the pendulum is l= 4a, and where o is the angle of rotation of the circle generating the cycloid. Show that the oscillations are exactly isochro- nous with a frequency wo = Vg/1, independent of the amplitude. *The reader unfamiliar with the properties of cycloids should consult a text on analytic geometry. PROBLEMS 139 2a m FIGURE 3-A Problem 3-8.
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