If you double the amplitude of a mass attached to a string, the time period of its motion will not change. The time period of an oscillating system depends on the length of the string and the acceleration due to gravity, but it is independent of the amplitude of the oscillation.
The time period of a mass attached to a string is determined by the equation:
T = 2π √(L/g)
where T is the time period, L is the length of the string, and g is the acceleration due to gravity.
Doubling the amplitude of the oscillation will only affect the maximum displacement of the mass from its equilibrium position, but it will not affect the time it takes to complete one full oscillation. The motion will still repeat with the same period as before.