A complex pendulum rolls without slipping on a circular track. The pendulum arm has mass m₂ and length L. The arm is pinned at point O. At point O, a torsional spring and damper (k and b) act on the pendulum. Additionally, a moment M(t) is applied to the pendulum at point O. At the distal end of the pendulum, a thin hoop of mass m₁ and radius r is attached to the pendulum. The hoop rolls without slipping on the circular track. The angle of the pendulum is denoted (t) and the rotational position of the hoop is denoted (t). Gravity acts on the system.
A complex pendulum rolls without slipping on a circular track. The pendulum arm has mass m₂ and length L. The arm is pinned at point O. At point O, a torsional spring and damper (k and b) act on the pendulum. Additionally, a moment M(t) is applied to the pendulum at point O. At the distal end of the pendulum, a thin hoop of mass m₁ and radius r is attached to the pendulum. The hoop rolls without slipping on the circular track. The angle of the pendulum is denoted (t) and the rotational position of the hoop is denoted (t). Gravity acts on 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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Generate the nonlinear EOM for the system using the energy method
Transcribed Image Text:A complex pendulum rolls without slipping on a circular track. The pendulum arm has
mass m₂ and length L. The arm is pinned at point O. At point O, a torsional spring and
damper (k and b) act on the pendulum. Additionally, a moment M(t) is applied to the
pendulum at point O. At the distal end of the pendulum, a thin hoop of mass m₁ and radius
r is attached to the pendulum. The hoop rolls without slipping on the circular track.
The angle of the pendulum is denoted (t) and the rotational position of the hoop is
denoted B(t). Gravity acts on the system.
Torsional Spring k
and
Torsional damper b
at rotation point O
Moment M(t) acting
at rotation point O
m₁
3
m₂, L
r
g
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