An elliptical hoop of negligible thickness with a vertical orientated semi-major axis a and a horizontal orientated semi-minor axis b, which has a mass per unit length of p, is mounted on a circular peg to which is attached a Carte- sian xy coordinate system in a vertical orienta- tion as shown in the accompanying sketch (the gravity g ellipse and peg are not rigidly joined to each other and are simply in kinematic contact with each other with negligible friction), such that the physical system lies within a flat ry plane. The ellipse is then allowed to freely oscillate in a to-and-fro rocking motion by a small angle 0, such that the gravitational acceleration g acts in a downwards direction that is parallel to the ellipse semi-major axis. 1.1 a 1.2 У onsidering the above system determine the following information clearly showing all steps and propriate reasoning: O Draw a free body diagram sketch of the system and annotate all relevant elements with explanations; Using the energy method (T+V) = const. where T is the kinetic energy and V is the potential energy derive the underlying equation of motion for the system by taking the angle as the independent variable that models the Single-Degree- of-Freedom (SDOF) vibration for the system;
An elliptical hoop of negligible thickness with a vertical orientated semi-major axis a and a horizontal orientated semi-minor axis b, which has a mass per unit length of p, is mounted on a circular peg to which is attached a Carte- sian xy coordinate system in a vertical orienta- tion as shown in the accompanying sketch (the gravity g ellipse and peg are not rigidly joined to each other and are simply in kinematic contact with each other with negligible friction), such that the physical system lies within a flat ry plane. The ellipse is then allowed to freely oscillate in a to-and-fro rocking motion by a small angle 0, such that the gravitational acceleration g acts in a downwards direction that is parallel to the ellipse semi-major axis. 1.1 a 1.2 У onsidering the above system determine the following information clearly showing all steps and propriate reasoning: O Draw a free body diagram sketch of the system and annotate all relevant elements with explanations; Using the energy method (T+V) = const. where T is the kinetic energy and V is the potential energy derive the underlying equation of motion for the system by taking the angle as the independent variable that models the Single-Degree- of-Freedom (SDOF) vibration for the system;
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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Transcribed Image Text:An elliptical hoop of negligible thickness with
a vertical orientated semi-major axis a and a
horizontal orientated semi-minor axis b, which
has a mass per unit length of p, is mounted
on a circular peg to which is attached a Carte-
sian xy coordinate system in a vertical orienta-
tion as shown in the accompanying sketch (the gravity g
ellipse and peg are not rigidly joined to each
other and are simply in kinematic contact with
each other with negligible friction), such that
the physical system lies within a flat zy plane.
The ellipse is then allowed to freely oscillate in
a to-and-fro rocking motion by a small angle 0,
such that the gravitational acceleration g acts
in a downwards direction that is parallel to the
ellipse semi-major axis.
1.1
a
Considering the bove system determine the following information clearly showing all steps
appropriate reasoning:
1.2
Y
Draw a free body diagram sketch of the system and annotate all relevant elements
with explanations;
Using the energy method (T+ V) =const. where T is the kinetic energy and V
is the potential energy derive the underlying equation of motion for the system
by taking the angle as the independent variable that models the Single-Degree-
of-Freedom (SDOF) vibration for the system;
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