In a simple harmonic oscillator, the angular frequency is directly proportional to the square root of the force constant divided by the mass of the oscillator. The force constant represents the stiffness of the oscillator, while the mass represents its inertia.
If the amplitude of the oscillator is doubled, it means that the maximum displacement from the equilibrium position is now twice the original value. This change in amplitude does not directly affect the angular frequency of the oscillator.
The angular frequency, denoted by ω, remains the same as long as the force constant and mass of the oscillator remain constant. Therefore, the multiplicative factor by which the angular frequency changes in this case is 1 (or no change).