Fun With The HP 27S

Fun With The HP 27S

Notes:

*  The HP 27S is set to FIX 4

*  Since none of the formulas have trigonometric functions, they can also be programmed on the HP 17B and HP 17BII+

Partial Fraction Decomposition

(A ∙ x + B)÷((x + C) ∙ (x + D)) = R÷(x + C) + S÷(x + D)

Inputs:  A, B, C, D

Outputs:  R, S

Formula:

PARTFRAC2:(A+B+C+D)×0=IF(S(R):(B-C×A)÷(D-C)-R:(B-D×A)÷(C-D)-S)

Example:  (4 ∙ x + 3) ÷ ((x - 5) ∙ (x + 1))

A = 4, B = 3, C = -5, D = 1

Results:  R = 3.8333, S = 0.1667

Use that the 0×(var1+var2+...) to set an order of variables in the solver.  

2 x 2 Simultaneous Equations

A ∙ x + B ∙ y = C

D ∙ x + E ∙ y = F

The solutions are:

x = (C ∙ E - B ∙ F) ÷ (A ∙ E - B ∙ D)

y = (A ∙ F - C ∙ D) ÷ (A ∙ E - B ∙ D)

Formula:

SIM2X2:0×(A+B+C+D+E+F+L(M:A×E-B×D))=IF(S(X):(C×E-B×F)÷G(M)-X:(A×F-C×D)÷G(M)-Y)

Example:  2x + 3y =5, -3x + 8y = -8

A = 2, B = 3, C = 5, D = -3, E = 5, F = -8

Results:  X = 2.5789, Y = -0.0526

Floor Function

floor(x):  the greatest integer less than or equal to x

floor(x):

If frac(x) = 0 Then return x

 Else If x≥0, then return intg(x) else return intg(x)-1

Formula:

FLOOR=IF(FP(X)=0:X:IF(X>=0:IP(X):IP(X)-1))

Examples:

X = 2.38, FLOOR = 2.0000

X = -9.21, FLOOR = -10.0000

Ceiling Function

ceil(x):  the least integer greater than or equal to x

ceil(x):

If frac(x) = 0 Then return x

  Else If x≥0, then intg(x)+1 else return intg(x)

Formula:

CEIL=IF(FP(X)=0:X:IF(X>=0:IP(X)+1:IP(X)))

Examples:

X = 2.38, CEIL = 3.0000

X = -9.21, CEIL = -9.0000

Rydberg Formula

The Rydberg formula measures the light's wavelength when an electron moves between energy quantum numbers (from higher to lower levels).  The Rydberg formula is to be used for simple atoms only, and is most used for hydrogen atoms.

1/λ = R ∙ Z^2 ∙ (1/n1^2 - 1/n2^2)

R = Rydberg's Constant ≈ 1.097373157 × 10^7 m^(-1)

Z = atomic number, 1 for hydrogen

n1, n2:  energy levels

Formula:

RYDBERG:INV(L)=1.09737316E7×SQ(Z)×(INV(SQ(N1))-INV(SQ(N2)))

N2 > N1

Example:

The energy of an hydrogen election from level 4 to level 2.  Z = 1

Z =1,  N1 = 2, N2 = 4

Result:  L = 4.8601E-7

Source:

Helmenstine, Todd. "What Is the Rydberg Formula and How Does It Work?" ThoughtCo, Aug. 28, 2020, https://www.thoughtco.com/what-is-the-rydberg-formula-604285   Retrieved November 4, 2021

Moment of Inertia - Circular Ring

D$OUT:  outside diameter

D$IN:  insider diameter.  For a circle, set D$IN = 0

I: moment of inertia

Formula:

I=PI×(D$OUT^4-D$IN^4)÷64

Examples:

Circular Ring:

D$OUT = 6.2, D$IN = 1.9;  I = 71.8935

Circle:

D$OUT = 6.2, D$IN = 0; i = 72.5332

Source:

"Properties Of Annual Sections" HP-19C/HP-29C Solutions: Civil Engineering  Hewlett-Packard.  1977

All original content copyright, © 2011-2022.  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. 

TI-84 Plus CE Programs from Casio FX-702P

TI-84 Plus CE Programs from Casio FX-702P

Notes

Here are several programs from the “Bilbliotheque De Programmes” for the Casio FX-702P translated for the Texas Instruments TI-84 Plus CE.  I understand that there is an English version of the book, but I have yet to find it online.  I am thankful to Google Translate since I am not fluent in French. 

I named each of the programs FX702P##, starting with 02.  Of course, use the program name that fits. 

Basic doesn’t translate directly to the TI-84 Plus programming language.  First of all, there are no line numbers for the TI-84 Plus, separate labels had to be created.  I added more descriptive lines to prompts and results strings because (1) the TI-84 Plus CE has a lot more programming space than the 1,680 bytes the Casio FX-702P offered, and (2) it helped me understand what the programs were. 

The reference page ties to the page in the document, not the PDF page. 

TI-84 Plus CE Program FX702P02  (ref. page 85)

Geometric Mean:  Enter 0 to stop data entry

"GEOMETRIC MEAN (85)"

"2018-05-20"

1→A:1→B

Lbl 20

Disp "X-",A

Input X

If X=0:Goto 60

A+1→A:B*X→B

Goto 20

Lbl 60

Disp "G=",B^(1/(A-1))

TI-84 Plus CE Program FX702P03 (ref. page 117)

Chemistry:  Analysis of an Acid

"ACID PRGM, 2018-05-20"

"(117)"

For(J,1,10)

Input "T= (0:END)",T

If T=0:Stop

37-T→T

Input "P*=",A

Input "PH=",P

Input "H=",H

.019T→B:A*10^(B)→A

Disp "P*=",A

P-.0146T→P:Disp "PH=",P

.0307A→C:C*10^(P-6.11)→D

Disp "(HC03­)=",D:Pause

D-(9.5+1.63H)(7.4-P)-24→C

(1-.0143H)C→B

Disp "BE=",B

(1+10^(P-6.11))→I:.0307AI→I

Disp "I=",I:Pause

End

TI-84 Plus CE Program FX702P04  (ref. page 131)

Accounting:  Calculate Accounts Receivable on outstanding invoices

"BILL REDUCTION (131)"

"2018-05-20 EWS"

1→Z:0→E:0→F

Lbl IN

"AMT: A"+toString(Z)+":"→Str1

Input Str1,A

"PERCENT: B"+toString(Z)+":"→Str1

Input Str1,B

"DAYS: C"+toString(Z)+":"→Str1

Input Str1,C

int(A*B/100*C/365+.5)→D

E+A→E:F+D→F

"AMT: D"+toString(Z)+":"→Str1:Disp Str1,D

Pause

Z+1→Z

Menu("MORE DATA?","YES",IN,"NO",NO)

Lbl NO

ClrHome

Disp "TOTAL INVOICES:",E

Disp "TOTAL INTEREST:",F

Input "COMMISSION:",X

E-F-X→N

Disp "NET RECIEVABLE:",N

TI-84 Plus CE Program FX702P05 (ref. page 73)

Thermal Stress

Disp "THERMAL STRESS"

"2018-05-22 EWS"

Disp "LINEAR EXPANSION","COEFFICIENT"

Input "L1:",L

Input "L2:",M

Disp "ELASTIC","COEFFICIENT"

Input "E1:",E

Input "E2:",F

Disp "CROSS SECTION"

Input "A1:",A

Input "A2:",B

Input "T:",T

EF(L-M)T→C

C/(EA+FB)→C

­(BC)→R:AC→S

ClrHome

Disp "THERMAL STRESS","A:","B:"

Output(2,5,R)

Output(3,5,S)

TI-84 Plus CE Program FX702P06  (ref. page 206)

Construction:  Concentrated Load on a Beam

Disp "BEAM FIXED AT","BOTH ENDS UNDER","CONCENTRATED LOAD"

"(63) 2018-05-22 EWS"

Degree

Input "YOUNG MOD (KG/MM^4):",E

Input "INERTIA (MM^4):",I

Input "LENGTH (MM):",L

Input "SUPPORT-LOAD DIST:",A

Input "LOAD (KG):",P

E*I→B

Input "INTEREST POINT:",X

If X≤A

Then:A→Y:X→Z

Else:L-A→Y:L-X→Z

End

Z(L+2Y)→C:P(L-Y)^2/L^3→D

D*Z*Z/6/B*(C-3*Y*L)→F

tan^-1(D*Z/2/B*(C-2*Y*L))→S

D*(C-Y*L)→M

D*C/Z→W

ClrHome:Fix 4

Disp "FLEXION (MM):"," ANGLE:"," TORQUE:","SHELL LOAD:"

Output(1,14,F)

Output(2,14,S)

Output(3,14,M)

Output(4,14,W)

Float

TI-84 Plus CE Program FX702P07 (ref. page 41)

Electronics:  Active Low-Pass Filter

Disp "ACTIVE LOW-PASS FILTER"

"(41) 2018-05-22 EWS"

Input "FREQ (HZ):",F

Input "AF:",A

Input "C1 (MICRO-F):",C

C/1E6→C

√(2)/(4*A*π*F*C)→R

A*R→S

S/(A+1)→T

2*(A+1)*C*1E6→U

ClrHome

Disp "R1:","R2:","R3:",C2:"

Output(1,5,R)

Output(2,5,S)

Output(3,5,T)

Output(4,5,U)

Source: Casio.  “Bibliotheque De Programmes FX-702P” (French document)  1985

You can find a PDF of the book in French on this page: http://casio.ledudu.com/pockets.asp?type=53&lg=eng .  Scroll down to the bottom of the page.  Also, shout out to the casio.ledudu.com page because it is an excellent site!

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

HP Prime: Diatomic Molecules

HP Prime: Diatomic Molecules

Diatomic Molecules

The program DIATOMIC will calculate:

*  Distance from the center of mass for each molecule

*  Inertia of the molecule

*  Rotational Energy at level j  (j = 0, 1, 2, 3…)

*  Vibrational Energy at level n  (n = 0, 1, 2, 3…)

A diatomic molecule is a molecule made of two atoms.  Examples are H₂, O₂, NaCl (sodium chloride), and CO (carbon monoxide). 

Input:

*  Mass of the two molecules, in atomic mass units (u).  The program will convert them to kilograms.  The conversion is 1 u ≈ 1.660538921 * 10^-27 kg

*  Distance of the “bar” between the two molecules.  Give this in ångströms, which an ångström is 10^-10 m. 

*  Rotational and Vibrational Energy levels.  They do not have to be the same.

*  Frequency of the diatomic molecule in 10^12 Hz.  Typically, molecules and atoms exhibit frequencies in the order of 10^13 Hz.

The formulas are derived from the use of the Schrödinger Equation.  While I won’t give much details, a derivation can be found in many resources, such as this link:  http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Rotational_Spectroscopy/Rotational_Spectroscopy_of_Diatomic_Molecules. 

This program can be adopted to other graphing calculators, but here is a version for the HP Prime:

Program DIATOMIC

EXPORT DIATOMIC()

BEGIN

// EWS 2015-07-09

// Diatomic Molecule

LOCAL m1,m2,r,l1,l2,I;

LOCAL j,n,w;

LOCAL Er,Ev;

// Input

INPUT({m1,m2,r,j,n,w},

"Diatomic Molecule",

{"Mass 1:","Mass 2:",

"r:","J:","N:","freq:"},

{"Mass in atomic units",

"Mass in atomic units",

"Distance in Angstroms",

"Rotational energy level",

"Vibration energy level",

"Frequency (10^12 Hz)"});

// Integer Parts

n:=IP(n);

j:=IP(j);

// Convert to kg

m1:=m1*1.660538921ᴇ−27;

m2:=m2*1.660538921ᴇ−27;

// Convert Angstroms to m;

r:=r/1ᴇ10;

// Convert to Hz;

w:=w*1ᴇ12;

// Lengths

l1:=m2*r/(m1+m2);

l2:=m1*r/(m1+m2);

// Inertia:

I:=m1*l1^2+m2*l2^2;

// Rotational Energy:

Er:=1.054571726ᴇ−34^2/(2*I)*j*(j+1);

// Vibrational Energy:

Ev:=(n+1/2)*1.054571726ᴇ−34*w;

// Results

PRINT();

PRINT("Distance to Center (m):");

PRINT("From Mol. 1: "+STRING(l1));

PRINT("From Mol. 2: "+STRING(l2));

PRINT("Inertia:");

PRINT(STRING(I)+" kg m^2");

PRINT("Rotational Energy:");

PRINT(STRING(Er)+" J");

PRINT("Vibrational Energy:");

PRINT(STRING(Ev)+" J");

RETURN({l1,l2,I,Er,Ev});

  

END;

  

Example

Mass 1:  Hydrogen:  1.00794 u

Mass 2:  Chlorine:  35.4270 u

Distance:  6 ångströms

Frequency:  3.6 x 10^13 Hz

Input Screen:

Output Screen:

Energy:

Rotational:  approx. 1.90*10^-23 J

Vibration:  approx. 5.69*10^-21 J

Sources:

Strong, Benjamin.  “Rotational Spectroscopy of Diatomic Molecules”  http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Rotational_Spectroscopy/Rotational_Spectroscopy_of_Diatomic_Molecules   March 26, 2015.   Retrieved July 5, 2015.

Wikipedia.  “Atom Vibrations”  https://en.wikipedia.org/wiki/Atom_vibrations  Retrieved July 9, 2015.

Young, Hugh D. & Roger A Freedman   “University Physics with Modern Physics”  11^th Ed.  Pearson:  San Francisco.  2003

  

Eddie

This blog is property of Edward Shore.  2015.