(a) Show by integration that the moment of incrtia ofa thin uniform rod, of mass m and length 20 ubout an axis through one end and perpendicular to the rod, isma (b) A thin unilunn rod AB of mass 3n and length 2a attached to a fixed hinge at the end A. hangs freely in cyuilibrium. The end B is given a small horizontal push so that the rod oscillates through a small angle in a vertical plane. (1) Show that the equation of motion of the rod can be expressed in the form 2d = 3g cos0+ K dr where 0 is the angle that AB makes with the downwanl vertical through A and Kis a constant. Find (ii) the radius of gyration of the rod about the axis through the hinge. (iii) the period of small oscillations of the rod. (iv) the length of the equivalent simple pendulum.

(a) Show by integration that the moment of incrtia ofa thin uniform rod, of mass m and length 20 ubout an axis through one end and perpendicular to the rod, isma (b) A thin unilunn rod AB of mass 3n and length 2a attached to a fixed hinge at the end A. hangs freely in cyuilibrium. The end B is given a small horizontal push so that the rod oscillates through a small angle in a vertical plane. (1) Show that the equation of motion of the rod can be expressed in the form 2d = 3g cos0+ K dr where 0 is the angle that AB makes with the downwanl vertical through A and Kis a constant. Find (ii) the radius of gyration of the rod about the axis through the hinge. (iii) the period of small oscillations of the rod. (iv) the length of the equivalent simple pendulum.

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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