Johannes Brahms
Sonata No. 1 Op.78 in G
violin and piano (1879)

Periodic Motion
Motion that repeats at regular intervals of time

Definitions
Oscillation
One complete round trip of the motion

Definitions
Period
The time required for one complete oscillation

Definitions
Frequency
The number of oscillations per second

Definitions
Equilibrium Position
The rest (or neutral)  position

Definitions
Displacement
The distance from the equilibrium position

Definitions
Amplitude
The maximum displace-ment (absolute value)

Units
Period - Time (Usually seconds)
Frequency - Oscillations (or cycles) per second
One cycle per second is called one Hertz  (Hz)

Units
Displacement - Distance
May be cm, m, ft, degrees, etc.
Amplitude - Distance
May be cm, m, ft, degrees, etc.

Equation 2.1
f = 1/T
or
T = 1/f

Experimental Observations
The frequency is independent of the amplitude
The greater the inertia factor, the less the frequency
The greater the stiffness factor, the greater the frequency

Experimental Observations

Equation  2.2
Relation between frequency and weight:

Equation  2.3
Relation between frequency and spring constant:

Experimental Observations
The frequency is independent of the amplitude
The greater the inertia factor, the less the frequency
The greater the stiffness factor, the greater the frequency

Resonance
Occurs whenever an oscillating system is driven at its natural frequency

Resonance
Under resonant conditions, a system oscillates at its maximum amplitude

Graphing

Phase
In Phase (0 degrees)
Out of Phase (180 degrees)
Measured in degrees