## 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)

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

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