Let angular frequency of SHM is ω and when is at distance x from mean position, its velocity will be given asv=ωA2−x2​⋅⋅⋅⋅⋅⋅⋅(i)When its velocity becomes double, let new amplitude is A′.So, 2v=ωA′2−x2​Putting the value of v from equation (i)2ωA2−x2​=ωA′2−x2​2A2−x2​=A′2−x2​⇒4(A2−x2)=A′2−x2⇒A′2=4A2−3x2⇒A′=4A2−3x2​