Answer
$E =\frac{4\pi^2FA^2}{\lambda}$
Work Step by Step
We know that the energy is given by:
$E=\mu \omega^2 A^2 vT$
$E=\frac{F}{v^2} \omega^2 A^2 vT$
$E=\frac{F}{v} \omega^2 A^2 T$
$E=\frac{F}{v} (\frac{2\pi}{T})^2 A^2 T$
$E=\frac{F}{v} (\frac{4\pi^2}{T}) A^2 $
$E =\frac{4\pi^2FA^2}{\lambda}$
