1. The problem statement, all variables and given/known data I don't have the exact wordings of the problem statement. I hope the following is enough to understand the problem. A solid hemisphere is kept on a plane horizontal frictionless surface. The hemisphere is made to tumble (or toss, I am not sure about the correct word). Find the time period of oscillation. The mass of hemisphere is M and radius is R. 2. Relevant equations 3. The attempt at a solution I have described the situation in the attachment. The CM of hemisphere is at a distance 3R/8 from the centre of base of hemisphere. To find the time period, I am thinking of writing down the expression for energy at any instant and then set its time derivative to zero. The orange coloured sketch is the new position of hemisphere. For the energy equation, I need the angular velocity, velocity of CM and height of CM from the ground. For angular velocity, I write ##d\theta/dt##. I can also find the height of CM but I have trouble finding the velocity of CM or specifically, the horizontal component of velocity. How do I find the horizontal displacement (##x##) of CM? I have found out rest of the variables in terms of ##\theta## and I am stuck on finding the horizontal displacement from hours. (I hope the sketch is easily decipherable). Any help is appreciated. Thanks!