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lecture34 - Simple Harmonic Motion Serway Chapter 15.1 15.2...

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1 Simple Harmonic Motion Serway Chapter 15.1, 15.2 Practice: Chapter 15, problems 1, 3, 5 Motion in the real world may not fit some of our earlier models (linear or circular motion, uniform acceleration). Many phenomena are repetitive or oscillatory . Example: Block and spring M Oscillatory Motion

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2 M Equilibrium: no net force M The spring force is always directed back towards equilibrium. This leads to an oscillation of the block about the equilibrium position. M For an ideal spring, the force is proportional to displacement . For this particular force behaviour, the oscillation is simple harmonic motion. x F = -kx Simple Harmonic Motion t x ( t ) t A t x ω cos ) ( = In Simple Harmonic Motion (SHM), the displacement is a sinusoidal function of time, e.g., : t A t x ω sin ) ( = or Question : Is a bouncing ball described by SHM?
3 t x ( t ) Three constants specify the motion: Amplitude, A : maximum displacement from the centre Angular Frequency, ω Initial phase (or phase constant), φ ) cos( ) ( φ ω + = t A t x In general, Phase The quantity ( ω t + φ )

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