Two simple harmonic motions of angular frequency 100 and 1000 rad ${\mathrm{s}}^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is

Acceleration of simple harmonic motion is

${\mathrm{a}}_{\max } = -{\mathrm{\omega }}^2\mathrm{A}$

or $\frac{{\left({\mathrm{a}}_{\max }\right)}_1}{{\left({\mathrm{a}}_{\max }\right)}_2} = \frac{{{\mathrm{\omega }}^2}_1}{{{\mathrm{\omega }}^2}_2}(\mathrm{as} \mathrm{A} \mathrm{remains} \mathrm{the} \mathrm{same})$

or $\frac{{\left({\mathrm{a}}_{\max }\right)}_1}{{\left({\mathrm{a}}_{\max }\right)}_2} = \frac{{\left(100\right)}^2}{{\left(1000\right)}^2} = {\left(\frac{1}{10}\right)}^2 = 1 : {10}^2$