1.32. An inverted pendulum is supported by a linear spring, as shown in Fig. 1.76. It is required to: (a) Derive the equation for the angular motion 0(t) about 0. (b) Determine the equilibrium positions. (c) Derive the differential equation for small angular motions 01 (t) about 8e for each equi- librium position. (d) Determine the stability nature of each equilibrium position. CARBONAMES k www m L FIGURE 1.76 Inverted pendulum supported by a

1.32. An inverted pendulum is supported by a linear spring, as shown in Fig. 1.76. It is required to: (a) Derive the equation for the angular motion 0(t) about 0. (b) Determine the equilibrium positions. (c) Derive the differential equation for small angular motions 01 (t) about 8e for each equi- librium position. (d) Determine the stability nature of each equilibrium position. CARBONAMES k www m L FIGURE 1.76 Inverted pendulum supported by a

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

1.32. An inverted pendulum is supported by a linear spring, as shown in Fig. 1.76. It is required
to:
(a) Derive the equation for the angular motion (t) about O.
(b) Determine the equilibrium positions.
(c) Derive the differential equation for small angular motions 01 (t) about 8e for each equi-
librium position.
(d) Determine the stability nature of each equilibrium position.
k
of
m
SD Ma
FIGURE 1.76
Inverted pendulum supported by a

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