The angular velocities of three bodies in SHM are w₁ w₂ w₃ with their respective amplitudes as A₁ A₂ A₃. If all three bodies have same mass and velocity then 
 

Velocity is the measure of a displacement's rate of change. The formula for a body's displacement (y) in the SHM with respect to angular velocity w is

$\mathrm{y}=\mathrm{asin\omega t}$

$\mathrm{velocity} \mathrm{v}= \mathrm{rate} \mathrm{of} \mathrm{change} \mathrm{of} \mathrm{displacement} =\frac{\mathrm{dy}}{\mathrm{dt}}$

$\mathrm{v}=\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}(\mathrm{asin} \mathrm{\omega t})=\mathrm{a\omega cos\omega t}$

Given, ${\mathrm{v}}_1={\mathrm{v}}_2={\mathrm{v}}_3 \mathrm{and} {\mathrm{a}}_1={\mathrm{A}}_1, {\mathrm{a}}_2={\mathrm{A}}_2,{\mathrm{a}}_3={\mathrm{A}}_3$

${\mathrm{A}}_1{\mathrm{\omega }}_1={\mathrm{A}}_2{\mathrm{\omega }}_2={\mathrm{A}}_3{\mathrm{\omega }}_3$

Hence the correct answer is ${\mathrm{A}}_1{\mathrm{\omega }}_1={\mathrm{A}}_2{\mathrm{\omega }}_2={\mathrm{A}}_3{\mathrm{\omega }}_3$.