The maximum acceleration of a particle in SHM is made four times keeping the  maximum speed to be constant. It is possible when

amax=Aω2   ......(1)vmax=Aω     ........(2)⇒amax=vmaxωSince,  vmax is constant, to make amax  four times, ω should be made four times.From (1), A should be made one-fourth.