Chaper 15 Oscillation Simple Harmonic Motion SHM n

Chaper 15, Oscillation Simple Harmonic Motion (SHM) n Spring and Pendulum n Damped and Forced Oscillation n

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

Velocity/Acceleration of SHM Partial Differential Equation (PDF)

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

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

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

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

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. a) What are the angular frequency, the frequency, and the period of the resulting motion? b) What is the amplitude of the oscillation? c) What is the maximum speed vm of the oscillating block, and where is the block when it occurs? d) What is the magnitude am of the maximum acceleration of the block? e) What is the phase constant for the motion? f) What is the displacement function x(t) for the spring block system?

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/s 2. a) What is the angular frequency of the system? b) What are the phase constant and the amplitude xm?