A spring mass system preforms $S.H.M.$ If the mass is doubled keeping amplitude same, then the total energy of $S.H.M.$ will become :
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The total energy of the mass spring system is equal to $\frac{1}{2} k A^{2},$ which is independent of mass. So the total energy will remain unchanged if amplitude is kept the same.
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Statement $II :$ It takes precisely one second to move between the two extreme positions.
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