Question

Introduction Many doors in public places are fitted with simple and inexpensive mechanisms that are designed to close the doors while reducing the slamming force to a minimum. Figure 1 Figure 1 depicts one such mechanism while Figure 2 provides a schematic description. The spring is mounted in order to push the door back to close once it is opened. The role of the hydraulic dashpot is to provide a viscous force that will prevent the door from slamming against the doorframe thus reducing the noise and physical damage.

Answer 1

Givens A SpOf clamped forced system Analysis ME GO to kg (=4 Ne R = 24 Nm for 61W ok alm M wift X w Using Newton's second law of system xt) and FBD ky M. ex ABD Mi = - kx- cx tf (t) > ft) Må tkx teỹ = f (D) Taking lapesce lapesce tearfounath Mg? x t RX®) + Cex®) fo (Ng? tk tes) x (8) 21 F G Pif 1) Output Input X 8) fel 11 (Mg? + k +18) Pf= (Bos2 +26+95) 2 Block diapsean abou system could be drawn as: th st(t) SCM ste kk

ai form of now input an applied inpulse of magnetnou fo face impulse systems State = fo. FAt=fo + K At: Response of system is qiuen by saving the EOM wd fou a feel system, fiq 2: Reifense of system - Ewnt x) = er Yoloswot txot Ewnxo riscosts where & ", Woe wolle yo wo clarken Ila & For impulse the response becomes Ewrt -0.011 X(t)= fa الحمامة mud 2126440 Skim= = 0.609 radi wda tez wn 0.60 con *1 0.0110.6047t fe Pes 0.60t 42. X(t) = 0.023F é e-6694103 is o bot

f USN Ft 45 د دے تا يه t Now this f(t) could be modelled as fict) + f(t) Foce a Mectarqulov putee espect, it cud be Ficta Response is given by: - Eunt Ewnto cos (Wdt-Ø) te t -45 X(t) = fo RST-62 [ c Cos Ewa CE-bod – 037 whole co ง $- test tents 0.011 1-06l12 c0.630. Created 1-62 Pustesg valles X=)= 0.034e-660x10*4 [-cos Co-6-068)te os forbe-2) – 01635 *02x10^2 ta X(t)

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