The equation for the velocity of an object performing simple harmonic motion is $v = {v_0}\sin \omega t$. Which of the following is a correct alternative form of the equation?

A. $v = {v_0}\sin \left( {\frac{{2\pi }}{T}} \right)t$
B. $v = {v_0}\sin \left( {\frac{t}{T}} \right)$
C. $v = {v_0}\sin \pi Tt$
D. $v = {v_0}\sin \left( {\frac{T}{{2\pi }}} \right)t$

A