(a) Starting from D’Alembert's principle, derive the differential equation of motion (in plane polar coordinates) for a simple pendulum (with inextensible string) exhibiting planar oscillations. Treat the oscillations as small oscillations.
(a) Starting from D’Alembert's principle, derive the differential equation of motion (in plane polar coordinates) for a simple pendulum (with inextensible string) exhibiting planar oscillations. Treat the oscillations as small oscillations.
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Transcribed Image Text:3. (a) Starting from D'Alembert's principle, derive the differential equation of motion
(in plane polar coordinates) for a simple pendulum (with inextensible string)
exhibiting planar oscillations. Treat the oscillations as small oscillations.
(b) Categorize each of the following constraint as either scleronomic or rheonomic.
i. A simple pendulum with its length changing with time as a given function
1(t).
ii. A cylinder rolling down without slipping on a rough inclined plane of angle
a.
iii. A particle sliding down the inner surface of a paraboloid of revolution having
its axis vertical and vertex downward.
iv. A bead is free to move along the length of a spoke in the bicycle wheel. The
wheel is rotating about its axis with a constant angular speed.
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