Answer :

Given


Therefore,



At the mean position, let 1kg block has velocity v.




After the 3kg block is gently placed on the 1kg, then 1kg+3kg=4kg block and the spring be one system. For this mass spring system, there is external force, the momentum should be conserved. Let 4kg block has velocity V.


Therefore initial and final momentum should be equal.




Now the two blocks have velocity 1/4 m/s at its mean position.



When the blocks are going to the extreme position, there will be only potential energy, (X new amplitude)




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