Harmonic Oscillations:

Simple Harmonic Oscillations -1 :
Key contents
Simple Harmonic Oscillations
Simple Harmonic Motions
Damped Oscillations
Forced Oscillations and Resonance
15.1 Oscillations
variations (What is varying?)
repeated → periodic
periodic variation → oscillation
Frequency of oscillation is the number of
oscillations that are completed in each second.
The symbol for frequency is usually f (or ν)
and its SI uit is Hertz (abbreviated as Hz).
It follows that
with T being the period.
Any oscillation that can be expressed with a
sinusoidal function is a harmonic oscillation.
When its amplitude is constant, it is a simple
harmonic oscillation.

That is,

x0 is the amplitude
t is the time
ω is the angular frequency,
φ is the phase constant or phase angle
(ωt+φ) is the phase
15.2 Simple Harmonic Oscillations
Some remarks for simple harmonic oscillations:
# good approximation to many things
# easy to manage analytically
# x(t) can be any physical quantity
# a projection of uniform circular motion
15.2 Simple Harmonic Oscillations
15.3 Simple Harmonic Motion
If the oscillating quantity is the position of an
object, the simple harmonic oscillation is a
simple harmonic motion (SHM).

SHM is the motion executed by a system subject
to a force that is proportional to the

displacement of the system but opposite in sign.

Simple Harmonic Motion -2:

Simple Harmonic Oscillator:

Damped Harmonic Motion:

Forced Harmonic Motion:

Forced Damped Harmonic Oscillators:


Waves and the One-Dimensional Wave Equation

Waves in more than one dimension

3D Wave Equation and Plane Waves

The Wave Equation

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