Chaper 15, Oscillation Simple Harmonic Motion (SHM) Spring and Pendulum
Chaper 15, Oscillation
Simple Harmonic Motion (SHM)
Spring and Pendulum
Damped and Forced Oscillation
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 v m block when it occurs?
of the oscillating block, and where is the d) What is the magnitude a m 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 x m
?
