An ideal spring oscillator has its amplitude doubled, with the same mass and spring. Sort each quantity by whether it changes.

Changes when the amplitude is doubled: The maximum displacement, The maximum speed, The total energy stored

Unchanged when the amplitude is doubled: The period, The frequency, The angular frequency omega

Since $\omega = \sqrt{k/m}$ contains no A, the period, frequency and angular frequency are all untouched, that is the defining and counterintuitive feature of simple harmonic motion. The displacement, the maximum speed (which is $A\omega$) and the stored energy (which goes as $A^{2}$) all depend on the amplitude.