1. The problem statement, all variables and given/known data Hi everybody! I'm trying to solve a basic problem about oscillations, but I struggle to get everything together when it comes to the differential equation...I hope someone can help me to understand it better :) A thin bar of mass m and length l is pivotable about its hanging point A, and can oscillate with the help of a spring (with spring constant k) attached to its other end. Consider there is no deflection. a) Put up the equation of movement and the resulting differential equation under the use of the displacement angle β. b) What is the time period T of the system? c) Give the amplitude A and the phase angle φ of the oscillation, if the bar is deflected at the angle β0 at time t = 0s and has an angle velocity ψ0. A possible approach to the resolution of the oscillation equation is β(t) = A⋅cos(ω0⋅t + φ). (see attached picture) 2. Relevant equations equations related to oscillation, moment of inertia of a bar, maybe torque and angular momentum 3. The attempt at a solution Okay this is probably very wrong, but I don't want to post the problem without at least trying something: a) I've learned how to derive the differential equation for a simple harmonic motion when the spring is horizontal, but I wonder if that still holds when it is vertical, because of the force of gravity? Maybe it is the case because "there is no deflection"? If so: m⋅a = - k⋅x ⇔ m⋅(d2x/dt) = - k⋅x(t) ⇔ m⋅(d2x/dt) + k⋅x(t) = 0 k = ω02⋅m ⇒ d2x/dt + ω02⋅x(t) = 0 But I believes that gives me for solution x(t) = A⋅cos(ω0⋅t + φ), right? Which is stated in the problem to the difference that it is for β(t)! I also feel the moment of inertia of the bar should play a role, since L = I⋅ω = I⋅β'. Using the parallel axis theorem I get I = ⅓⋅m⋅l2 but I don't dare to go any further because I don't really understand what I am doing.. Could someone give me a clue or briefly describe me how to tackle such problems? Thank you very much in advance. Julien.