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HW2 - M.E 8207 Homework#2 1 A rectangular door has height h...

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M.E. 8207 Homework #2 1. A rectangular door has height h , thickness d , width l , and mass m . It is fitted with an automatic door closer which consists of a torsional spring with a modulus k . Determine the necessary damping to critically dampen the return swing of the door. Use numerical values h = 2m, d = 40mm, l = 0 . 75m, m = 36kg, and k = 10 Nm/rad. If the door is opened 90 0 and released, how long will it take until the door is within 1 0 of closing? (For the last part, you will need MATLAB.) 2. A rigid massless rod of length l carries a mass m at one end, and is connected to the wall by a torsional spring of stiffness k as shown in Fig. 1. A damper with viscous damping coeﬃcient c is connected to the rod at a distance a from the wall. (a) Assume small displacements and derive the equation of motion. It may be as- sumed that the torsional spring is connected to the rod in such a way that it does not exert a moment when the rod is horizontal.

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