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Chapter13 - Chapter13:PeriodicMotion 2. Simple harmonic...

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Chapter 13:  Periodic Motion
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2. Simple Harmonic Motion Simple harmonic motion: Motion that follows a repetitive pattern, caused by a restoring force that is proportional to displacement from the equilibrium position.
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Hooke’s law : F kx = -
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( ) cos( ) x t A t ϖ φ = + A: amplitude T: Period: Time to complete one full cycle of motion. f : frequency : Number of cycles of motion per second. ω: angular frequency ϕ : phase constant 2 2 , T T π π ϖ ϖ = = 1 T f =
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Period and phase
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Velocity and Acceleration ( ) ( ) dx t v t dt = = ( ) ( ) dv t a t dt = = 2 F ma m x ϖ = = -
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Circle reference
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To find the phase angle and the amplitude from initial condition : x 0 , v 0
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Example 13.2) By attaching a spring balance to the free end and pulling toward the right, a force of 6.0 N causes a displacement of 0.030 m. a) Find the spring constant. We attach a 0.50 kg glider to the end and pull it a distance of 0.020 m and release it. b) Find the angular frequency, frequency, and period of the oscillation
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Example 13.3) Consider the similar system in Example 13.2 with
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