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Statement of a problem № 3431

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Consider a pendulum consisting of a small mass m attached to one end of an inextensible cord of length l rotating about the other end which is fixed. The pendulum moves on a spherical surface. Hence the name spherical pendulum. The inclination angle f in the xy-plane can change independently. (a) Obtain the equations of motion for the spherical pendulum. (b) Discuss the conditions for which the motion of a spherical pendulum is converted into that of (i) simple pendulum and (ii) conical pendulum.

Solution:
Consider a pendulum consisting of a small mass m attached to one end of an inext

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