Harmonic Oscillator- Is this correct?

[kubaanglin]

Homework Statement

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What is the shortest time required for a harmonic oscillator to move from $x = A$ to $x = \frac{A}{2}$? Express your answer in terms of the period $T$.

Homework Equations

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$x(t)=Acos(\omega t)=Acos(2\pi\frac{t}{T})$

The Attempt at a Solution

$A=Acos(0)$ which means $\frac{t}{T}=$ whole number
$\frac{A}{2}=Acos(\frac{\pi}{3})$ which means $\frac{t}{T}=\frac{1}{6}$
$t=\frac{T}{6}$

 

[Charles Link]

Very good. It looks correct to me.