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AP Unit I F 1

AP Unit I F 1. Simple Harmonic Motion (dynamics and energy relationships.). Reference Chapter 13.1-13.5. 1. Students should understand simple harmonic motion, so they can:

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AP Unit I F 1

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  1. AP Unit I F 1 Simple Harmonic Motion (dynamics and energy relationships.)

  2. Reference Chapter 13.1-13.5 • 1. Students should understand simple harmonic motion, so they can: • a) Sketch or identify a graph of displacement as a function of time, and determine from such a graph the amplitude, period, and frequency of the motion. • b) Write down an appropriate expression for the displacement of the form A sin ωt to describe the motion.

  3. d) State the relations between acceleration, velocity, and displacement, and identify points in the motion where these quantities are zero or achieve their greatest positive and negative values.

  4. g) State how the total energy of an oscillating system depends on the amplitude of the motion, sketch or identify a graph of kinetic or potential energy as a function of time, and identify points in the motion where the energy is all potential or all kinetic. • h) Calculate the kinetic and potential energies of an oscillating system as functions of time, sketch or identify graphs of these functions, and prove that the sum of the kinetic and potential energy is constant.

  5. ω = θ/t θ= ωt θ R = A x = A cos ωt

  6. Velocity and Displacement • sin θ = vx/v0 v = -ωA sin ωt • sin θ = ((A2 – x2))/A v0 v = (v0/A)(A2 – x2) vx A θ 90-θ x

  7. Acceleration and Displacement • a = -ω2x = -ω2 A cos ωt • acceleration is always proportional to displacement directed towards equilibrium

  8. x = A cos ωt v= -ω A sin ωt a = - ω2 A cos ωt

  9. Oscillating horizontal spring • ½ kA2 = ½ mv2 + ½ kx2

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