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Chaper 15, Oscillation

Chaper 15, Oscillation. Simple Harmonic Motion (SHM) Spring and Pendulum Damped and Forced Oscillation. Oscillations Simple Harmonic Motion (SHM). Angular frequency. Period. Simple Harmonic Motion. Velocity/Acceleration of SHM.

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Chaper 15, Oscillation

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  1. Chaper 15, Oscillation • Simple Harmonic Motion (SHM) • Spring and Pendulum • Damped and Forced Oscillation

  2. Oscillations Simple Harmonic Motion (SHM) Angular frequency Period Simple Harmonic Motion

  3. Velocity/Acceleration of SHM Partial Differential Equation (PDF)

  4. Newton’s 2nd Law Newton’s 2nd law Hooke’s law Angular frequency Period

  5. Pendulum The Simple Pendulum Physical Pendulum (Will derive the equations on the board as examples).

  6. Damped and Forced Oscillations 1. Damped Oscillation (add a friction force) 2. Forced Oscillation and Resonance Oscillation will be enhanced significantly when the natural frequency of oscillation = frequency of external force

  7. Example of Solar Filament Oscillation (Discovered by BBSO/NJIT)

  8. Sample Problem 15 – 1 A block whose mass m is 680 g is fastened to a spring whose spring constant k is 65 N/m. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 cm on a frictionless surface and released from rest at t = 0. • What are the angular frequency, the frequency, and the period of the resulting motion? • What is the amplitude of the oscillation? • What is the maximum speed vm of the oscillating block, and where is the block when it occurs? • What is the magnitude am of the maximum acceleration of the block? • What is the phase constant  for the motion? • What is the displacement function x(t) for the spring block system?

  9. Sample Problem 15– 2 At t = 0, the displacement x(0) of the block in a linear oscillator is –8.50 cm. The block’s velocity v(0) then is –0.92 m/s, and its acceleration a(0) is +47.0 m/s2. • What is the angular frequency  of the system? • What are the phase constant  and the amplitude xm?

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