1. The problem statement, all variables and given/known data An equation of motion for a pendulum: (-g/L)sinΦ = Φ(double dot) 2. Relevant equations L = length g = gravity ω = angular velocity Φο = initial Φ 3. The attempt at a solution The solution is Φ=Asinωt+Bcosωt solving for A and B by setting Φ and Φ(dot) equal to zero respectively gives: Φ= Φοcosωt My question is how can you just go ahead and write down Φ=Asinωt+Bcosωt? My professor said it was because this was the only function that when differentiated twice give -sinωt but I can't just take that for what it is because I need to know how to arrive there.