The total mechanical energy of a spring-mass system in simple harmonic motion is 
suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
Total mechanical energy of a spring-mass system of mass m and angular frequency ω in simple harmonic motion is
According to question, the mass become twice. Hence,
New mass m’=2m and angular frequency ω will be 
Therefore, the new mechanical energy (E’) will
Which is same as old Total mechanical energy.
Note: k does not changes as spring used for both are same.
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