1. The problem statement, all variables and given/known data The periodic motion is given in the form: f(t) = Acos(wt+φ) What is the amplitude and phase constant for the harmonic oscillator when: (a) f(t) represents position function x(t) (b) f(t) represents velocity function v(t) (c) f(t) represents acceleration function a(t) 2. Relevant equations x(t) = Acos(wt+φ) v(t) = -wAsin(wt+φ) a(t) = -w2Acos(wt+φ) 3. The attempt at a solution (a) To find amplitude from a position equation, I know that amplitude is the maximum displacement of the particle in harmonic oscillation, so A=x(t) To get A=x(t), I would need my phase of motion to be zero, so that cos(wt+φ)=1. This would occur when φ=0 and t=0. Therefore A=x and φ=0 However, I'm not really sure why it's relevant to ask the amplitude and phase constant for the velocity and acceleration functions. Both amplitude and phase constant (φ) are determined from initial conditions, so wouldn't the amplitude and phase constant be the same for x(t), v(t) and a(t), given that it's based off the same function?