Answer:
When both initial speed and initial displacement is doubled then amplitude will be doubled. 
Explanation:
Given that :- Amplitude of simple harmonic Oscillator  is doubled.
So, 
      Formula of Simple harmonic oscillator is   ...........(1)
  ...........(1)
                                                             Where X = Position in (m,cm,km.....) 
                                                                         A = Amplitude  in (m,cm,km.....) 
                                                                         F = Frequency in (Hz)
                                                                         T = Time in (sec.)
                                                                         Ф = Phase in (rad)
   For initial displacement taking t=0 we get,
                            Initial displacement =  .................(2)
    .................(2)            
Now taking equation (1) and differentiating it w.r.t to (t) we get
                                 
                                  
taking t=0 for initial speed then we get, 
                                 Initial speed =  ...............(3)
    ...............(3)
observing equation (2) & (3) that the initial displacement and initial speed depends on the Amplitude of the Oscillator.
Hence,
when both initial speed and displacement is doubled then amplitude will be doubled.