1. The problem statement, all variables and given/known data Hi everyone! Here is a new problem about oscillations! Thx to all of you, I'm definitely making progress in the field. Let's see how that problem goes: A pendulum of mass m is hanging on a string of length L and is "pushed" by a spring with spring constant k. At the deepest point of the pendulum (that is, when α = 0), the spring is compressed at x0 of its equilibrium position. a) determine the equation of motion of the angle α (for the case α<<1). b) the solution of the equation is α(t) = A⋅sin(ω⋅t) + B⋅cos(ω⋅t) + αR. Find the angular frequency and the angle αR (equilibrium position) in terms of m, L, and k. c) what is the solution, when the pendulum goes at t=0 from the position α = 0? Check out the two attached picture. The 1st one describes the problem while the 2nd one shows my interpretation of the situation. 2. Relevant equations Equation of motion, oscillations, torque 3. The attempt at a solution a) At (2) (see pic), m⋅x'' = -k⋅x ⇔ x'' + (k/m)⋅x = 0 ΣD = FF ⇒ α'' = -(k⋅x)/(m⋅L) For a small angle we can say that (x/L) ≈ α, so the equation of motion goes: α'' + (k/m)⋅α = 0 I'm pretty confident that it is correct, but let's see about b) : I can input the solution to the equation in my equation for t=0, and after simplifying the cos and sin I get: -B⋅ω2 + (k/m)⋅B + (k/m)⋅αR = 0 I do the same for α(0) and I find that αR = 2⋅B. I input that in the previous equation and get, quite easily: ω = √(3k/m) Now I've tried a few things, mixing equations and states, but I can't get my hands on αR! Could someone give me a clue in what direction I should look? For c) I'm not sure I understand the question right. Isn't it what I have already done in B on the way of solving for ω? Thank you very much in advance for your advices, I appreciate it! Julien.