In Figure 1 a perfectly rigid rod with the known mass of m and length of...
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In Figure 1 a perfectly rigid rod with the known mass of m and length of 3a is pivoted at point P. Point C shows the location of the center of the rod's mass. A mass M is attached to the end of the rod and is pulled down by gravity. For the horizontal orientation of the rod, the angle = 0, the displacement y = 0, and the spring is in neither tension nor compression. Assuming that y is a small displacement and that remains always a small angle, answer the following questions: m Figure 1: System schematic. M Your tasks: A Draw the FBD for the rod (4 pts) B Considering as the dynamic variable, derive the equation of motion in its input-output standard form. To present the EOM in its standard form, you should move the inputs and constant forces to the right and keep things related to the dynamic variable and its derivatives on the left. Write out the mass moment of inertia of the system about the point P, IP, as a function of the given variables. (4 pts) C Present the EOM obtained in the previous part as a function of y, the linear coordinate associated with the point mass at the end of the rod, instead of 0. (4 pts) D Using each dynamic variable, and y, derive expressions for the static displacement of the system and name them as Vat and 8t, respectively. (4 pts) In Figure 1 a perfectly rigid rod with the known mass of m and length of 3a is pivoted at point P. Point C shows the location of the center of the rod's mass. A mass M is attached to the end of the rod and is pulled down by gravity. For the horizontal orientation of the rod, the angle = 0, the displacement y = 0, and the spring is in neither tension nor compression. Assuming that y is a small displacement and that remains always a small angle, answer the following questions: m Figure 1: System schematic. M Your tasks: A Draw the FBD for the rod (4 pts) B Considering as the dynamic variable, derive the equation of motion in its input-output standard form. To present the EOM in its standard form, you should move the inputs and constant forces to the right and keep things related to the dynamic variable and its derivatives on the left. Write out the mass moment of inertia of the system about the point P, IP, as a function of the given variables. (4 pts) C Present the EOM obtained in the previous part as a function of y, the linear coordinate associated with the point mass at the end of the rod, instead of 0. (4 pts) D Using each dynamic variable, and y, derive expressions for the static displacement of the system and name them as Vat and 8t, respectively. (4 pts)
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Related Book For
Fundamentals of Physics
ISBN: 978-0471758013
8th Extended edition
Authors: Jearl Walker, Halliday Resnick
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