1. The problem statement, all variables and given/known data Determine the angular frequency of the system in the image. The cable is ideal but the pulley is not. I will present the same solution but with different coordinate axes. For some reason they arent the same and neither of them are correct. Given data: R is the radius of the pulley. K is the spring constant. m is the mass of the block. Icm is the moment of inertia of the pulley in form of a disk with respect to the center of mass of the pullet. Variables: T is the tension, w is the angular frequency. a and α will be translational acceleration and rotational acceleration. 2. Relevant equations ΣF=ma torque = (moment of inertia) * (angular acceleration) Through the differential equation i can get the angular frequency w^2 3. The attempt at a solution I have trouble with the signs. If I am not wrong, I should establish a system of coordinates and stay with it throughout the problem. I will work on two different coordinate axes to show that I can't reach the solution and both are different. Something about my operation is wrong. To get the angular frequency I decide to displace the block X meters lower than its position of equilibrium. The magnitude of the spring force kx will be different in my view because if I put X axis pointing upward, then the displacement it would be positive and so |KX| should be KX. If I put X axis pointing downward then it would be |KX| = -KX The correct answer is in the image and i cant seem to reach it. I hope i can get some help.