The below figure shows a uniform circular disc compound pendulum of mass m and radius a which is pivoting around point O. If the disc were to be displaced by a small angular displacement from its equilibrium position, find: 1. The equation of motion (EOM) of the disc for small angular displacements. 2. The natural frequency of the disc. 3. The values of b for which the above determined natural frequency is maximum.

Does Mary have a valid concern about the pump?

As an engineering student, your community has asked you to assist an architect in designing a building fit for winter and summer. Apply your knowledge of mechanical engineering science (Thermofluid) in the design.  Kindly include the following:i. Specify the type of building (domestic or community centre)ii. Specify the capacity of the water (in volume) for the buildingiii. Include the vapour compression refrigeration cycle componentsiv. Suggest and discuss the source (s) of energy for the buildingv. Discuss the possible type of fuel to be used and give a reason for the usagevi. Include a sketch with key components