Notes
Outline
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