Nodal Equations Flashcards
Parts to a nodal equation
y=A(trig(Bx+C)+D
A- amplitude, vertical stretch
B- Horizontal stretch (Angular Frequency)
C- horizontal shift
D- vertical shift
Trig- a trig function, usually sine or cosine
Graphing trig-functions
1) Create graph with respect to time
2) Start at x=hShift. If sine, y=vShift. If cosine, y=amplitude+vShift
3) Calculate period from the frequency. Mark the above y-value at every frequency multiple on x
4) If sine, mark that y-value between the frequency multiples too. If cosine, mark those frequency midpoints with yValue-(2*amplitude)
5) If sine, mark the first frequency quarter point with (amplitude+vShift), alternating between positive and negative for each half-frequency measure thereafter. If cosine, mark the frequency quarter points with the y-value in the middle of the y-values on either side.
6) Connect all of the points with a smooth curve
The trigonometry of a nodal function
Either sin or cosine, almost never given in tangent
Derivative series for nodal function
Sin→Cos→-Sin→-Cos→repeat
Rate
Expressed as the quotient of two dirivatives
i=dq/dt
Current
Velocity, rate at which electrons flow through a given point
i=dq/dt
Amp=coulombs per second
Voltage
Rate of Energy per charge, strength of electron motion
v=dw/dq
Volt=kg(m^2)/(sec^2)
Accumulation
Always the integral of a function in respect to its x-variable
Also can be written as multiplication
Energy
Accumulation of current with time
q=∫idt
Power
P=v*i
Watts=
Phase
Portion of the nodal equation in the parentesis, to be taken as sin, cos, or tan
Always in radians usually have to convert to degrees
Angular frequency
Horizontal stretch factor of your nodal equation
Period
Time it takes to complete one whole cycle, Seconds per cycle
T=1/f
Frequency
How many cycles are completed in one second, often a decimal/fraction
f=1/T
Node
The ‘zeros’ in your nodal equation
