Chaper 15, OscillationOscillations Simple Harmonic Motion (SHM)Velocity/Acceleration of SHMNewton’s 2nd LawPendulumDamped and Forced OscillationsExample of Solar Filament Oscillation (Discovered by BBSO/NJIT)Sample Problem 15 – 1Sample Problem 15– 2Chaper 15, OscillationChaper 15, OscillationSimple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)Spring and PendulumSpring and PendulumDamped and Forced OscillationDamped and Forced OscillationOscillations Oscillations Simple Harmonic Motion (SHM)Simple Harmonic Motion (SHM)PeriodPeriodAngular Angular frequencyfrequencySimple Harmonic MotionSimple Harmonic MotionVelocity/Acceleration of SHMVelocity/Acceleration of SHMPartial Differential Equation (PDF)Partial Differential Equation (PDF)Newton’s 2Newton’s 2ndnd Law LawNewton’s 2Newton’s 2ndnd law lawHooke’s lawHooke’s lawPeriodPeriodAngular frequencyAngular frequencyPendulumPendulumThe Simple PendulumThe Simple PendulumPhysical PendulumPhysical Pendulum(Will derive the equations on the board as (Will derive the equations on the board as examples).examples).Damped and Forced OscillationsDamped and Forced Oscillations1. Damped Oscillation1. Damped Oscillation(add a friction force)(add a friction force)2. Forced Oscillation and Resonance2. Forced Oscillation and Resonance Oscillation will be enhanced Oscillation will be enhanced significantly when the natural frequency of significantly when the natural frequency of oscillation = frequency of external forceoscillation = frequency of external forceExample of Solar Filament Oscillation Example of Solar Filament Oscillation (Discovered by BBSO/NJIT)(Discovered by BBSO/NJIT)Sample Problem 15 Sample Problem 15 – 1– 1A block whose mass A block whose mass mm is 680 g is fastened to a spring whose spring is 680 g is fastened to a spring whose spring constant constant kk is 65 N/m. The block is pulled a distance is 65 N/m. The block is pulled a distance x x = 11 cm from = 11 cm from its equilibrium position at its equilibrium position at xx = 0 cm on a frictionless surface and = 0 cm on a frictionless surface and released from rest at released from rest at tt = 0. = 0.a)a)What are the angular frequency, the frequency, and the period of the resulting What are the angular frequency, the frequency, and the period of the resulting motion?motion?b)b)What is the amplitude of the oscillation?What is the amplitude of the oscillation?c)c)What is the maximum speed What is the maximum speed vvmm of the oscillating block, and where is the of the oscillating block, and where is the block when it occurs?block when it occurs?d)d)What is the magnitude What is the magnitude aamm of the maximum acceleration of the block? of the maximum acceleration of the block?e)e)What is the phase constant What is the phase constant  for the motion? for the motion?f)f)What is the displacement function What is the displacement function x(t)x(t) for the spring block system? for the spring block system?Sample Problem 15Sample Problem 15– 2– 2At At tt = 0, the displacement = 0, the displacement x(0)x(0) of the block in a linear of the block in a linear oscillator is oscillator is –8.50 cm. The block’s velocity –8.50 cm. The block’s velocity v(0)v(0) then is then is –0.92 m/s, and its acceleration –0.92 m/s, and its acceleration a(0)a(0) is +47.0 m/s is +47.0 m/s22..a)a)What is the angular frequency What is the angular frequency  of the system? of the system?b)b)What are the phase constantWhat are the phase constant  and the amplitude and the amplitude