Standard content

A workshop for the harder side of oscillations, at the level of JEE Advanced, A-Level Physics and IB Higher Level. Springs with pulleys and moving supports, rods, wires and liquids, small swings found from an energy curve, two motions added together, and damped and driven oscillators with the quality factor. It goes beyond the three free courses and ends with a full timed paper.

What's inside

1. Springs, pulleys and moving supports: A spring system can be tied up with pulleys, carried on a trolley, loaded with a lump or stacked with a second block. The method is always the same. Find the energy for a small move, or the restoring force, and read off the effective spring constant and the middle of the swing.
2. Rigid bodies, liquids and the energy curve: Rods, wires, liquids, floating bodies and particles in an energy well all oscillate by the same rule. Write the energy for a small move. The curvature of the potential energy sets the stiffness, and the inertia of the moving parts sets the mass. The square root of their ratio is the angular frequency.
3. Adding motions, damping and driving: Two simple harmonic motions can be added along a line, which gives beats, or at right angles, which gives Lissajous figures. A damping force makes the amplitude fall, and the quality factor counts how slowly. A driving force at the right frequency builds a large swing, whose size and phase follow the quality factor.