Question

Some doors have a mechanical device to either manually or automatically close them, usually without undue noise. https://en.wikipedia.org/wiki/Door_closer Consider one such device when viewed from above. A door with mass m, width w, and height h, has a door closer attached a distance d from the hinge. Model the door closer as a linear spring with constant k and damper with constant c. Assume the spring is unstretched when the door is closed. Consider only spring and damper displacement in the j-direction, and assume that their forces act only in the j-direction. The schematic below at right models the door, viewed from above a) Derive the nonlinear EOM for this system b) Linearize the EOM assuming θ is small c) Find the undamped natural frequency. d) Decide where the door closer should be attached by determining the value of d that results in critically damped behavior.

ANS to arrive at:

Answer 1

Date Sol - fre Sody diagram ot 36 d cose k(dsin9) 2 2 1 2 3 ,'Z Moment about 0 :0 for lireosige the Equathn assu me amall oscillatiovn

Da Unckumped Natusal freayency uun Lea ear 3