oscillations
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The simple harmonic oscillations (SHO) of suspended solid bodies are related to their geometry. The torsional pendulum oscillates in the horizontal plane; the SHO does NOT depend on the small angle approximation. In this lecture Professor Lewin discusses the SHO equation of motion for a rigid body pendulum, for a liquid sloshing in a U-shaped tube, and for a torsional pendulum.
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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especial...more
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Systems consisting of pendulums and springs can freely oscillate at their natural frequencies (also called normal modes). When we expose a system to a wide spectrum of frequencies, the response will be very large at the normal mode frequencies (resonances) of that system. Examples include musical instruments (standing waves on violin strings and pressure waves in wind instruments), and torsional standing waves on a bridge driven by strong winds.
