text: simple harmonic motion? i'm having a bit of an issue figuring out what the time and the phase constant would be for this homework problem below for the first part:  a particle moves in simple harmonic motion with a frequency of 2.50 oscillations/s and an amplitude of 5.00 cm. (a) through what total distance does the particle move during one cycle of its motion in cm ? (b) what is its maximum speed in cm/s? (c) what is the maximum acceleration in m/s^2?  i don't actually need the answers figured out.  i'm thinking that i just take the derivative of the equation for part a for part b (the velocity) and then the second derivative for the acceleration... but like i said, i'm completely clueless about what i would plug in for time and the phase constant.  this is the equation i'm using btw:  x = a cos(angular acceleration * time + phase constant)  i figured 2.50 = 1/t, t=.4 angular acceeration = 2pi/t = 15.71  any ideas? you have a problem with your formula. in fact, you should write:  x = a cos(angular speed * t) the 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.  the 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.  now 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. so: a: 20 cm (particle moves from +5 to -5 to +5) b: 78.54 cm/s c: 1234 cm/s^2 = 12.34 m/s^2