I'm trying to derive an equation for the velocity and acceleration of an object undergoing simple harmonic motion.
I have the equation for displacement: $x = A\sin (2 \pi ft)$
If I differentiate the equation with respect to $t$ then I should get an equation for the velocity and if I differentiate again, I should get an equation for the acceleration, right?
So if I differentiate once, I get: $v = 2 \pi f\cos (2 \pi ft)$
If I differentiate again, I get: $a = -2 \pi fsin (2 \pi ft)$
However, I don't think these equations are correct. Am I making a silly mistake?
N.b. This isn't homework, I'm making extra revision notes :P