# Simple harmonic motion

a particle of mass m moving in such manner that its displacement x varies with time t following equation x = a sin wt. ( w = omega )
where a and w are constants.
what is the average KE for the motion of the particle in one rev?

isnt the answer suppose to be 1/2 mw(sq)a(sq) ?

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In my physics class, to solve a problem like that, we used the equation KE=(1/2)m*v^2. So, when given the equation for x, take the derivative to get velocity, and insert it into the equation.

yeah, that is how they derive the equation
1/2 mw^2 a^2.

i use that way, but the answer is 1/4mw^2 a^2

HallsofIvy
Given a continuous function, its "average value" on an interval from a to b is $$\frac{\int_a^b f(x)dx}{b-a}$$