6.16. Tilting plane *** A mass M is fixed at the right-angled vertex where a massless rod of length is attached to a very long massless rod (see Fig. 6.19). A mass m is free to move frictionlessly along the long rod (assume that it can pass through M). The rod of length is hinged at a support, and the whole system is free to rotate, in the plane of the rods, about the hinge. Let be the angle of rotation of the system, and let x be the distance between m and M. Find the equations of motion. Find the normal modes when and x are both very small. Fig. 6.19 1 x M m

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.