Saturday, July 24, 2021

HP 48G: Multiple Equation Solver and The Equation Library

HP 48G: Multiple Equation Solver and The Equation Library 





Calculators Featured:  HP 48G, HP 48G+, HP 48GX


The Equation Solver


Any program in the HP 48G family, we can set up the calculator to solve a set of equations.  The commands involved:


STEQ:  Store a list of equations in the variable EQ.  The variable EQ is used in the solver.


MINIT:  This command initializes the solver.  The system variable MPAR is created.


MITM:  This optional command allows the solver to have a custom title and arrange the variables in a custom order.  Arguments:  2:  title string, 1:  the list of variables.  The list can have a blank string, " ".  All the variables must be included.  


MSOLVR:  Starts the solver.


In the solver:


( var ):  store

[ left shift ] ( var ):  solve

[ right shift ] ( var ):  recall


An RPL Template:


<< ... 

{ list of equations }  STEQ MINIT

"title" { list of variables } MITM

MSOLVR

... >>


HP 48G Program:  HCURVE


<<  DEG

'T=R*TAN(Δ/2)'

'L=R*Δ*π/180'

'C=2*R*SIN(Δ/2)'

3 →LIST STEQ MINIT

"Horizontal Curve"

{ Δ R T L C } MITM

MSOLVR >>


Variables:


Δ = central angle (in degrees)

R = central radius

T = tangent length

L = arc length of the horizontal curve

C = chord length


One of Δ or R must be known.  When Δ and R are both entered or solved for, L, T, and C can be solved for.


Example 1:


Inputs:

Δ: 45

R: 100


Outputs:

T = 41.4213562373

L = 78.5398163398

C = 76.536686473


Example 2:


Inputs:

L:  1706

Δ: 54


Outputs:

R = 181.012221943

T = 2.2303337494

C = 164.35658198


The Equation Library


The equation library can be accessed by pressing [ right shift ] [ 3 ].  A list of various subjects are listed.  Options:


[ F1 ] (SI):  SI units are used

[ F2 ] (ENGL):  English units are used

[ F3 ] (UNIT): turn units on and off


Once a topic is selected, another menu s presented where all the equations are contained.  Depending on the topic, one or more equations are selected.  When ready, select (SOLV).  


Example 1:  Triangle


Plane Geometry -> Triangle -> Equation 2 of 6


A=(b*h)/2

P=b+√(v^2+h^2)+√((b-v)^2+h^2)





Example:  (default SI units are used)


Inputs:

P: 100 cm

b: 40 cm

h: 35 cm


Outputs:

V = 20 cm

A = 700 cm^2


Example 2:  Longitude Waves


Waves -> Longitudinal Waves -> Equation 1 for 4


s = sm cos( k * x - ω * t )

v = λ * f

k = 2 * π / λ

ω = 2 * π * f


Example:  (default SI units are used)


Inputs:

λ: 0.2264 cm

f: 1400 Hz

t: 15 s

sm: 1.5 cm


Outputs: 

v = 314.44 m/s

k = 0.279750013677 r/cm

ω = 8976.45943005 r/s


Eddie


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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