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hw1 - 4 A rigid bar is pinned at its left end and supported...

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Homework 1 1. Problem 1.2 in the textbook. Note that since the hoop is smooth, there is no friction force. The problem statement suggests summing forces in the transverse (or tangential, or circumferential) direction, because this direction is perpendicular to the unknown normal force. You must take into account the horizontal centripetal acceleration due to the hoop’s rotation about the vertical axis. 2. Problem 1.5 in the textbook. We started this problem as an example problem in the lecture. 3. Problem 1.7 in the textbook. Think of how you can sum forces or moments on the bar in such a way that the unknown forces from the circular surface do not contribute. When you find these unknown forces, they should be in terms of , , and , which would be found by solving the (ordinary differential) equation of motion that you derived.
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Unformatted text preview: 4. A rigid bar is pinned at its left end and supported by two springs as shown. Find the equivalent spring constant that relates the force F to the vertical displacement at the right end of the bar. 5. Verify the expression in Table 1.2 for the equivalent spring constant for a uniform pinned-pinned beam with a force at midspan. Derive the beam deflection from the ordinary differential equation , where is the bending moment in the beam resulting from the concentrated midspan load. 6. Problem 1.29 in the textbook, but let the beam be pinned at both ends, rather than fixed. Are the beam and spring in parallel or in series? 7. Problem 1.30 in the textbook....
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