Answer: No, The energy will remain the same
Explanation: Doubling the mass and leaving the amplitude unchanged won't have any effect on the total energy of the system.
At maximum displacement, E=0.5kA^2
Where E = total energy
K = spring constant
A = Amplitude
From the formula above : Total Energy is independent of mass,. Therefore, total energy won't be affected by Doubling the mass value of the object.
Also when the object is at a displacement 'x' from its equilibrium position.
E = Potential Energy(P.E) + Kinetic Energy(K.E)
P.E = 0.5kx^2
Where x = displacement from equilibrium position
E = Total Energy
K. E= E-0.5kx^2
From the relation above, total energy is independent of its mass and therefore has no effect on the total energy.