1. The problem statement, all variables and given/known data For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion. 2. Relevant equations x(t) = A*cos(ωt) (SHM mathematical model) v(t) = -Vmax*sin(ωt) Fave = 1/(b-a)∫f(x)dx 3. The attempt at a solution As soon as i get started with this problem, I hit a brick wall. I don't know if this is due to me being brain-dead because of all the studying I've been doing today, but whatever it is I can't seem to wrap my head around it! the problem: How do I calculate the average velocity? I know v(t) is the derivative of x(t) I also know the average value function shown above. 1.) find derivative of x(t) to get v(t) v(t) = -Vmax*sin(ωt) 2.) use average value function on v(t) to find "average velocity" since Vavg is defined as the average velocity of one cycle, and one cycle = 2pi b = 2pi a = 0 Fave = 1/(2pi - 0)*∫v(t)dt = 0 this makes the equation impossible to prove! no SHM has a Vmax of 0! yet..... how could the average velocity NOT be zero? What am I doing wrong here?