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Chapter13 - Chapter 13 Periodic Motion 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. ϖ : 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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3. Energy in Simple Harmonic  Motion Potential Energy Total mechanical energy ( ) U t = E =
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Example 13.2) Mass m=0.50 kg. Find a) the force constant of the spring b) the angular frequency, the period of the oscillation Now, the initial displacement is changed to 0.015 m and the initial velocity is 0.40 m/s c) Find the amplitude, and phase angle
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