What is the best way to go about solving a SHM problem that asks for amplitude and phase constant when only one initial condition (x(0)) is given? I'm a little confused because I read that to find A and the phase constant you must use the initial conditions - but I've encounter a few problems which only give one initial condition. I'm obviously missing some understanding... here's an example: 1. The problem statement, all variables and given/known data You observe a vibration that has a frequency of 45 Hz. At t = 0 the displacement is 20 mm and at t = 7 ms the displacement is -12 mm. What is the amplitude (A) and phase constant (⌀) for the equation x(t) = Acos(ωt + ⌀) 2. Relevant equations x(t) = Acos(ωt + ⌀) T = 1/f ω = 2πf = 2π/T 3. The attempt at a solution ω = 2πf ω = 2π(45) ω = 282.7 rads/s x(t) = Acos(ωt + ⌀) x(0) = 0.02 = Acos((282.7)(0) + ⌀) 0.02 = Acos(⌀) A = 0.02/cos(⌀) Now what? Do I do the same with x(0.007) even though A and ⌀ are supposed to be found using initial conditions? Any help is appreciated.