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Two bodies are connected with a spring and one of the particles is given a velocity v find 1* maximum velocity of second particle and 2* max. extension in the spring. Answer fast please!
when velocity is given to one body the that time the amplitude of oscillations will be maximum compression in the spring . At the time of maximum compression, velocities of both the bodies will be equal say V1. and this velocity be the velocity of the second body at the of release after compression. so by law of conservation of momentum ---
m1*v = (m1+m2)V1 if the mass of bodies is m1 and m2
so V1 = (m1*v) / (m1+m2) ------------------------------------(i)
by the conservation of energy
1/2m1*v^2 = 1/2kx^2+1/2(m1+m2)V1^2 ----------------------(ii)
where k is the spring constant and x is the max compression. after the release this will be the max. extension.......
by solving (i) and (ii)
x= [m1m2v^2/k(m1+m2)]^1/2

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