In simple harmonic motion, the amplitude does not depend on the mass of the object. The amplitude represents the maximum displacement from the equilibrium position during oscillation, and it is determined by the initial conditions of the system and not by the mass.
The mass does, however, affect other properties of simple harmonic motion. The mass affects the period (T) of the oscillation, which is the time taken for one complete cycle. The period can be calculated using the formula:
Period (T) = 2π√(m/k)
where m is the mass of the object and k is the spring constant or the restoring force constant.
When the mass is doubled while keeping other factors constant, such as the spring constant, the period of the oscillation will change. According to the equation above, the period of the oscillation will increase since it is directly proportional to the square root of the mass. This means that the oscillations will take longer to complete one cycle.
However, it's important to note that the amplitude will remain the same even if the mass is doubled.