text: You have a problem with your formula. In fact, you should write:\n\nx = A cos(angular speed * t)\nThe phase angle is not relevant to this problem. You are only concerned about complete cycles of the harmonic motion and there is no other particle or timing reference, so the question of phase shift doesn't arise.\n\nThe number to use for "angular speed" is derived from the statement that the particle makes 2.5 oscillations/s. One oscillation corresponds to 2*pi of angular motion and takes 0.4 seconds. Therefore you know that every 0.4 seconds, (angular speed)*0.4*n = n*2*pi. So (angular speed) = 2.5*2*pi. Angular speed calculated like this will have units of radians/s. You calculated the right value, 15.71, but you didn't have the right understanding.\n\nNow you can answer the questions. The first falls out directly from getting the right equation for x. And you are correct that the second and third parts are answered by successive differentiations of x, then finding the maximum. So the amplitude for displacement is A; the amplitude for velocity is A*(angular speed); for acceleration it is A*(angular speed)^2.\nSo: a: 20 cm (particle moves from +5 to -5 to +5)\nb: 78.54 cm/s\nc: 1234 cm/s^2 = 12.34 m/s^2