Page 1 Oscillatory Motion ? Object attached to a spring ? Simple harmonic motion ? Energy of a simple harmonic oscillator ? Simple harmonic motion and circular motion ? The pendulum Page 2 Oscillatory Motion ? Object attached to a spring ? Simple harmonic motion ? Energy of a simple harmonic oscillator ? Simple harmonic motion and circular motion ? The pendulum An Object Attached to a Spring kx F s ? ? kx ma x ? ? x m k a x ? ? When acceleration is proportional to and in the opposite direction of the displacement from equilibrium, the object moves with Simple Harmonic Motion. Page 3 Oscillatory Motion ? Object attached to a spring ? Simple harmonic motion ? Energy of a simple harmonic oscillator ? Simple harmonic motion and circular motion ? The pendulum An Object Attached to a Spring kx F s ? ? kx ma x ? ? x m k a x ? ? When acceleration is proportional to and in the opposite direction of the displacement from equilibrium, the object moves with Simple Harmonic Motion. Equation of Motion x m k dt x d a ? ? ? 2 2 ? ? ? ? ? ? ? ? t A t x cos Second order differential equation for the motion of the block The harmonic solution for the spring-block system m k ? ? where Page 4 Oscillatory Motion ? Object attached to a spring ? Simple harmonic motion ? Energy of a simple harmonic oscillator ? Simple harmonic motion and circular motion ? The pendulum An Object Attached to a Spring kx F s ? ? kx ma x ? ? x m k a x ? ? When acceleration is proportional to and in the opposite direction of the displacement from equilibrium, the object moves with Simple Harmonic Motion. Equation of Motion x m k dt x d a ? ? ? 2 2 ? ? ? ? ? ? ? ? t A t x cos Second order differential equation for the motion of the block The harmonic solution for the spring-block system m k ? ? where Some Terminology ? ? ? ? ? ? ? ? t A t x cos Amplitude Angular frequency Phase constant Phase } Page 5 Oscillatory Motion ? Object attached to a spring ? Simple harmonic motion ? Energy of a simple harmonic oscillator ? Simple harmonic motion and circular motion ? The pendulum An Object Attached to a Spring kx F s ? ? kx ma x ? ? x m k a x ? ? When acceleration is proportional to and in the opposite direction of the displacement from equilibrium, the object moves with Simple Harmonic Motion. Equation of Motion x m k dt x d a ? ? ? 2 2 ? ? ? ? ? ? ? ? t A t x cos Second order differential equation for the motion of the block The harmonic solution for the spring-block system m k ? ? where Some Terminology ? ? ? ? ? ? ? ? t A t x cos Amplitude Angular frequency Phase constant Phase } Properties of Periodic Functions ? The function is periodic with T. ? The maximum value is the amplitude. ? Angular Frequency (rad/s) ? ? 2 1 ? ? f T Period (s) ? ? 2 ? f Frequency (1/s=Hz) ? / ? ? ? ? ? T t x t x ? ?Read More

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