In simple harmonic motion, the total mechanical energy of given system is $$E$$. If mass of oscillating particle $$P$$ is doubled then the new energy of the system for same amplitude is

For SHM, total energy is

$$E=\frac{1}{2}kA^2$$

where

Notice mass does not appear in this expression.

If mass is doubled, $$m\to2m$$, angular frequency changes:

$$\omega=\sqrt{\frac{k}{m}}$$

so it becomes smaller, but energy depends only on k and A.

Since amplitude is same, energy remains unchanged:

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