Answer
See explanation.
Work Step by Step
If the amplitude is doubled, the object must move twice the total distance in one period: instead of going from A to 0 to –A to zero back to A, it now moves from 2A to 0 to –2A to zero back to 2A.
The period of SHM is unaffected by a change in amplitude.
The maximum speed is the angular speed (unaffected) multiplied by the amplitude (which has now doubled). The maximum speed is doubled.
The object must cover more distance in the same time, so it makes sense that it must reach a higher maximum speed.
