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El_Psy_Congroo!!
7.
here you have variable force:- F=-kx ... it depends on position.
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this is strange ... the bullet emerges with almost same veclocity http://www.wolframalpha.com/input/?i=sqrt%282%281%2F2*0.005*400^2+-+900*0.05^2%2F2+%29%2F0.005%29
for this .. just remember PE of spring is \[ {1 \over 2}kx^2\]