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 function1(t).ii. A cylinder rolling down without slipping on a rough inclined plane of anglea.iii. A particle sliding down the inner surface of a paraboloid of revolution havingits axis vertical and vertex downward.iv. A bead is free to move along the length of a spoke in the bicycle wheel. Thewheel is rotating about its axis with a constant angular speed.

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Answered: (a) Starting from D’Alembert's…

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(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.