Answer
$v_m^2 = a_m~A$
Work Step by Step
We can write an expression for $v_m^2$:
$v_m^2 = (A~\omega)^2 = A^2~\omega^2$
We can write an expression for $a_m$:
$a_m = A~\omega^2$
Then:
$v_m^2 = A^2~\omega^2 = (A~\omega^2)~A = a_m~A$
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