High School Differentiating some simple harmonic equation

[Trance-]

So I was just trying to differentiate (for no good reason) the equation :
x=x₀sin(wt)
(w= angular frequency, x₀= maximum displacement, t=time)

to obtain the expression :
a= -w²x

I differentiated twice with respect to time the initial expression for x and got:
a= -w²x₀sin(wt)

I must have done something wrong while differentiating... so help me out, folks.

 

[axmls]

I'll write it in a more suggestive manner:
$$a = -\omega^2 (x_0 \sin(\omega t))$$
Notice anything?

 

[Trance-]

I'll write it in a more suggestive manner:
$$a = -\omega^2 (x_0 \sin(\omega t))$$
Notice anything?

Oh crap!
My sleep deprivation must be taking its toll dammit. Thanks a lot man!
I make the dumbest mistakes.