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lecture04 - Oscillations 1 Different types of motion...

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Oscillations 1. Different types of motion: Uniform motion 1D motion with constant acceleration Projectile motion Circular motion Oscillations 2. Different types of oscillations: Periodic oscillations Chaotic oscillations A motion is called periodic when the system comes back to the same physical conditions every time interval T. Harmonic oscillations (the simplest, the most important type of periodic oscillations)
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3. Harmonic oscillations Relation between circular motion and simple harmonic oscillations x y θ φ ϖ θ cos A x t = + = θ f T π π ϖ 2 2 = = A a A v A x 2 max max max ϖ ϖ = = = x a 2 ϖ - = ( 29 ( 29 ( 29 φ ϖ ϖ φ ϖ ϖ φ ϖ + - = + - = + = t A a t A v t A x cos sin cos 2 R=A Period of SHO is independent from amplitude! linear equation
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A=x max T ϖ φ - = t max max 0 a a v x x = = - = 0 0 max = = = a v v x 0 0 max = - = = a v v x x t t v a t max max 0 a a v x x - = = =
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4. Hook’s law and simple harmonic motion kx ma - = k m f T π ϖ π 2 2 1 = = = Hook’s law: Newton’s second law: Simple harmonic motion: = - = ma F kx F x a 2 ϖ - = x m
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