Ch 10 Simple Harmonic Motion and Elasticity

Ch 10 Simple Harmonic Motion and Elasticity - Chapter 10...

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Chapter 10 Simple Harmonic Motion and Elasticity
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Goals ± To follow periodic motion to a study of simple harmonic motion. ± To solve equations of simple harmonic motion. ± To use the pendulum as a prototypical system undergoing simple harmonic motion. ± To study how oscillations may be damped or driven. ± To study stress, strain and elastic deformation. ± To define elasticity and plasticity.
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10.1 The Ideal Spring and Simple Harmonic Motion The ideal spring and simple harmonic motion Hooke’s Law (ideal spring) K is the“ stiffness constant ”, spring constant ” or “ force constant x is the length change (displacement) caused by stretch (or squish) of the spring from its natural unstretched (unstrained) length. The minus sign in Hooke’s law reminds us that the direction of the force exerted by the spring is opposite the displacement (stretch or squish) that produces it ( restoring force ). x k F Applied x =
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Using an Air Track
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+ x + x + x L o L o L o L o x x x x F s + x F s F s F s When the spring is compressed , the force increases in direct proportion to the amount of compression . A spring with natural (unstrained) length L o When the spring is stretched , it exerts a “restoring force in direct proportion to the amount of stretch.
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A large value for k means the spring is “stiff” in the sense that a large force is required to stretch or compress it. External Forces : Gravitational Force. Normal Force. Frictional Forces. Tension Force. Restoring Force of a Spring. Newton’s Second Law Σ F = m a When the restoring force has the mathematical form F = k x , the type of friction-free motion is designated as simple harmonic motion .”
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10.1 The Ideal Spring and Simple Harmonic Motion Example 1 A Tire Pressure Gauge The spring constant of the spring is 320 N/m and the bar indicator extends 2.0 cm. What force does the air in the tire apply to the spring? () ( ) N 4 . 6 m 020 . 0 m N 320 = = = x k F Applied x
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10.1 The Ideal Spring and Simple Harmonic Motion Hooke’s Law Restoring force of an ideal spring The restoring force on an ideal spring is x k F x =
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When an object moves in simple harmonic motion, a graph of its position as a function of time has a sinusoidal shape with an amplitude A. A pen attached to the object records the graph.
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10.2 Simple Harmonic Motion and the Reference Circle t A A x ω θ cos cos = = Displacement The ball mounted on the turntable moves in uniform circular motion, and its shadow, projected on a moving strip of film, executes SHM
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A top view of a ball on a turntable. The ball’s shadow on the film has a displacement x that depends on the angle θ through which the ball has moved on the reference circle. For simple harmonic motion, the graph of displacement x versus time t is a sinusoidal curve, The period T is the time required for one complete motional cycle.
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Ch 10 Simple Harmonic Motion and Elasticity - Chapter 10...

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