Answer
Since both the distance and the average speed are proportional to the amplitude, the period of the mass-spring system is independent of the amplitude.
Work Step by Step
The distance traveled during each cycle is proportional to the amplitude. However, the maximum acceleration, the maximum speed, and the average speed are also proportional to the amplitude.
We can write an expression for the period $T$:
$T = \frac{d}{v_{ave}}$
Since both the distance and the average speed are proportional to the amplitude, the period of the mass-spring system is independent of the amplitude.
