Lecture_17

# Lecture_17 - Pull on it it will pull back – restorative...

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Harmonic Motion & Elasticity

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Harmonic Motion An object moves along a repeated path – oscillatory motion. Characterized by amplitude and period (or frequency, or angular frequency) Examples: Pendulum (swing), spring, celestial orbits When the path is sinusoidal, the motion is simple harmonic motion (SHM)
Quantification f = 1 T θ=ω t T = 2 π ω y = A sin θ y = A sin ( 2 π f t )

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SHM
Speed of a Point on a Rotating Object v y = v c cos θ v c = 2 π A T = 2 π f A v y = 2 π f A cos ( 2 π f t ) v x =− 2 π f A sin ( 2 π f t ) x = A cos ( 2 π f t ) a c = v c 2 A a y = a c sin θ=( 2 π f ) 2 A sin ( 2 π f t ) a x =− a c cos θ=−( 2 π f ) 2 A cos ( 2 π f t )

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Mass on a Spring F =− kx = ma x = A cos ( 2 π f t ) a x =−( 2 π f ) 2 A cos ( 2 π f t ) kA = m ( 2 π f ) 2 A f = 1 2 π k m What is the period of oscillation? T = 1 f
Pendulum F restore = F parallel =− mg sin θ sin θ≃θ , θ= y L F parallel = m g y L = m a f = 1 2 π g L , ( k = mg L )

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Harmonic Motion and Energy Example: What is the maximum speed of the oscillating object?
Push on a block of metal, it will push back.

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Unformatted text preview: Pull on it, it will pull back – restorative force. Hooke's Law works for objects other than springs More deformation with “softer materials”. Characterized by Young's (or elastic) modulus (Table 11.1). Δ L negative – compressive force Δ L positive – tensile force F A = Y Δ L L Stress Strain Shear & Bulk Works with translational (shear) strains also but with different moduli, S. F A = S Δ x L Works with bulk strains (those that tend to change the size of an object) also but with different moduli, B P =− B Δ V V Since all of these strains create a restoring force, one should expect that they may cause harmonic motion (just like a spring). Damping Driven Oscillator...
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Lecture_17 - Pull on it it will pull back – restorative...

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