Question

B- The damping for the recoil mechanism of the below system is a critical damping, the maximum recoil distance is 0.4m upon firing, Find the value of the initial recoil velocity. And also find the time taken by the gun to return to a position 0.1m from its initial position. Total mass (gun barrel+recoil mechanism)=500kg Recoil-mechanism spring and oil-filled damper k=10000N/m

Answer 1

+ Giotwayo) è unt. Response of critically clamped system X(t)- G+Ct) e-Wnt By Initial conditions 2(4+0)5 % and iſt=e) =. C=Xo C2 = rotondo act)= [+0+ 20+o+wn Xo) ä(t)= %6e wnt Ewn).+ 6+W Xo)t twe -wst. e -winst e å(t)=0 For max response We get with hot wnto) nowne wat (%ot wnpot one ē wat = 0 wat e. [rown -Xown - footwnto) t wnt footwnto)] (ho twaro) + twn- nown = t(no+wn xo) n = Hownt potwino) nown +lio + Wn xo) hotwnnown ti 2070 t åo %own =ty wy

so r(t) = K tě Wnt, Given maximum recoil distance Xman = 0.4m xtp = [70+ (xotwnyo) 4:] e wnt, 710 =0 for maximum value of a wntuso) ( :t; un e a &max= ko iton) Home no e. aman sio x max whe 10000 X e O. Y X = 500 = 0.4x4,4721 X 2.718 4,865 mb Initial no recal reloaly -inta X(t = (ão twn xoltz e ) a (tz) = lotze Wntz Given altz) =0.1m Ool = 4.865Xtz 4:472 tz t₂ = 0, 8258 sec Time laken by gun to return position gooim