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PHYS16 – Lecture 32 Ch. 15 Oscillations

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Oscillations pre-question Is a bouncing ball an example of simple harmonic motion? A)Yes B)No

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Oscillations pre-question Two kids are swinging on two swings of the same height – one kid is a little chubbier than the other. Neglecting frictional forces, which kid completes a back and forth swing in the fastest time? A) The chubby kid B) The skinny kid C) The kid who pushes off the ground the best D) Both complete in the same time

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Outline for Oscillations Simple Harmonic Motion – Position, Velocity, Acceleration – Force – Energy Resonance and Damping

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Oscillations and Periodic Motion Simple Harmonic Motion 1) About Equil. 2) Periodic 3) Sinusoidal

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Discussion: Examples of SHM? Mass on a Spring Pendulum Snowboarder in halfpipe Bungee jumper Child on swing Bobble head doll?

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Simple Harmonic Motion: Position, Velocity, Acceleration

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Simple Harmonic Motion Equilibrium Point

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Discussion: Phase Your book says that displacement is in terms of cosine and I just said that it is in terms of sine? Who is right? There is also a phase term (φ) that let’s you set the initial condition. If the oscillation starts at A it is a sine with a φ=90 degrees or a cosine with a φ=0 degrees.

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SHM Position, Velocity, Acceleration

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Discussion What is the max speed and when does it occur? Equilibrium Point

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Example Question An object undergoes simple harmonic motion. If the amplitude and period are doubled, the object’s max speed is: A)Quadrupled B)Doubled C)Unchanged D)Halved E)Quartered

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Simple Harmonic Motion: Restoring Force

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Restoring Force Force that always points back to the equilibrium position – Example = spring k is just a constant – for a spring it is the spring constant

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Restoring Force – Spring

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Discussion: Period A block on a spring has a period of T. What is the period if: A)the mass is doubled? B)k is quadrupled? C)A is doubled?

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Restoring Force - Pendulum What is the period of a pendulum?

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Simple Harmonic Motion: Energy

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Energy in SHM

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Main Points - SHM Movement Restoring Force creates oscillation Energy is dependent on amplitude

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