An object-spring system undergoes simple harmonic motion with an amplitude a. does the total energy change if the mass is doubled but the amplitude isn't changed (t/f)

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.