A pendulum consists of a mass m at the end of a massless stick of length e. The other end of the stick is made to oscillate vertically with a position given by y(t) = A cos(at), where A << . See Fig. 6.12. It turns out that if is large enough, and if the pendulum is initially nearly upside- down, then surprisingly it will not fall over as time goes by. Instead, it will (sort of) oscillate back and forth around the vertical position. If you want to do the experiment yourself, see the 28th demonstration of the entertaining collection in Ehrlich (1994). Find the equation of motion for the angle of the pendulum (measured relative to its upside-down position). Explain why the pendulum doesn't fall over, and find the frequency of the back and forth motion.
A pendulum consists of a mass m at the end of a massless stick of length e. The other end of the stick is made to oscillate vertically with a position given by y(t) = A cos(at), where A << . See Fig. 6.12. It turns out that if is large enough, and if the pendulum is initially nearly upside- down, then surprisingly it will not fall over as time goes by. Instead, it will (sort of) oscillate back and forth around the vertical position. If you want to do the experiment yourself, see the 28th demonstration of the entertaining collection in Ehrlich (1994). Find the equation of motion for the angle of the pendulum (measured relative to its upside-down position). Explain why the pendulum doesn't fall over, and find the frequency of the back and forth motion.
A pendulum consists of a mass m at the end of a massless stick of length e. The other end of the stick is made to oscillate vertically with a position given by y(t) = A cos(at), where A << . See Fig. 6.12. It turns out that if is large enough, and if the pendulum is initially nearly upside- down, then surprisingly it will not fall over as time goes by. Instead, it will (sort of) oscillate back and forth around the vertical position. If you want to do the experiment yourself, see the 28th demonstration of the entertaining collection in Ehrlich (1994). Find the equation of motion for the angle of the pendulum (measured relative to its upside-down position). Explain why the pendulum doesn't fall over, and find the frequency of the back and forth motion.
Introduction to Classical Mechanics
Please solve using equation of motion. Thank you.
Transcribed Image Text:Fig. 6.12
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Transcribed Image Text:6.5. Inverted pendulum ****
A pendulum consists of a mass m at the end of a massless stick of length
e. The other end of the stick is made to oscillate vertically with a position
given by y(t) = A cos(@t), where A << . See Fig. 6.12. It turns out
that if is large enough, and if the pendulum is initially nearly upside-
down, then surprisingly it will not fall over as time goes by. Instead, it
will (sort of) oscillate back and forth around the vertical position. If you
want to do the experiment yourself, see the 28th demonstration of the
entertaining collection in Ehrlich (1994).
Find the equation of motion for the angle of the pendulum (measured
relative to its upside-down position). Explain why the pendulum doesn't
fall over, and find the frequency of the back and forth motion.
Branch of physics that focuses on the motion of an object when subjected to external forces. The object will be in equilibrium when the external forces are balanced.
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