How does adding mass to a spring system affect its amplitude?

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Adding mass to a spring system does not affect the amplitude of oscillation in simple harmonic motion (SHO) when the mass is at its maximum position. The potential energy stored in the spring at this point is independent of the mass attached, meaning that doubling the mass does not change the amplitude. The energy remains constant, as it is determined by the spring constant and the displacement from equilibrium. Therefore, the amplitude of the new system remains the same as the original. This conclusion aligns with the principles of energy conservation in SHO.
Dr. S
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Homework Statement



You have a horizontal spring system such that it undergoes SHO on a frictionless surface. with a known mass attached at the end of the spring. When that mass reaches its maximum position (amplitude) a second identical mass is dropped on top of the initial, effectively doubling the mass of the system (all other mass shall be considered negligible). What is the amplitude of the new system?

The Attempt at a Solution



The same as before?

When the initial mass is at its amplitude position, it has all its energy stored as potential energy which does not depend on mass. Therefore, adding mass will not affect this potential energy and thus won't affect amplitude.

Is this right?
 
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I'd love some help with this one, it's really been bugging me.
 
Your argument looks fine, and your conclusion correct.
 

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