TI-55 III Programs Part III: Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency

TI-55 III Programs Part III:  Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency

For Part I, click here:  Digital Root, Complex Number Multiplication, Escape Velocity

For Part II, click here:  Impedance of a Series RLC Circuit, Quadratic Equation, Error Function  

TI-55 III:  Area and Eccentricity of the Ellipse

Formulas:

Assume a>b, where a and b represent the lengths of semi-diameters, respectively

Area:  A = π*a*b

Eccentricity:  ϵ = √(1 – (b/a)^2)

Program: 

Partitions Allowed: 1-5

STEP	CODE	KEY	COMMENT
00	71	RCL	R0 = a
01	00	0
02	65	*
03	71	RCL	R1 = b
04	01	1
05	65	*
06	91	π
07	95	=
08	12	R/S	Display A
09	53	(
10	01	1
11	75	-
12	53	(
13	71	RCL
14	01	1
15	55	÷
16	71	RCL
17	00	0
18	54	)
19	18	X^2
20	54	)
21	95	=
22	13	√
23	12	R/S	Display ϵ

Input:  a [STO] 0, b [STO] 1, [RST] [R/S]

Result:  Area, [R/S] Eccentricity

Test:  a = 7.06, b = 3.78

Result: A ≈ 83.839055, ϵ ≈ 0.8445918

TI-55 III:  Determinant and Inverse of 2 x 2 Matrices

This program will require 4 registers. 

Input Matrix:  M = [[ R0,  R1 ] [ R2 , R3 ]]

Output Matrix:  M^-1 = [[ R3/det, -R1/det ] [ -R2/det, R0/det ]]

Where det = R0 * R3 – R1 * R2  (determinant). 

Program: 

Set 4 partitions:  [2^nd] [LRN] (Part) 4

STEP	CODE	KEY	COMMENT
00	71	RCL	Calculate determinant
01	00	0
02	65	*
03	71	RCL
04	03	3
05	75	-
06	71	RCL
07	02	2
08	75	*
09	71	RCL
10	01	1
11	95	=
12	12	R/S	Display determinant
13	61	STO	Calculate inverse
14	55	÷
15	00	0
16	61	STO
17	55	÷
18	03	3
19	94	+/-
20	61	STO
21	55	÷
22	01	1
23	61	STO
24	55	÷
25	02	2
26	01	1	Display 1 to indicate “done”
27	12	R/S

Input:  Store:

M(1,1) [STO] 0

M(1,2) [STO] 1

M(2,1) [STO] 2

M(2,2) [STO] 3

Press [R/S] to calculate the determinant of M.  If M≠0, continue and press [R/S].

You will see a 1 in the display, this is used as an indicator that the program is done. 

Result Inverse Matrix:

M^-1[1,1] stored in R3

M^-1[1,2] stored in R1

M^-1[2,1] stored in R2

M^-1[2,2] stored in R0

Test: 

M =  [ [ -1.4,  3.0 ], [ 2.8, 6.4 ] ]

Determinant = -17.36

M^-1 ≈  [ [ -.3686635945, .1728110599 ], [ .1612903226, .0806451613 ] ]

TI-55 III: Speed of Sound/Fundamental Resonant Frequency

Formulas:

Speed of Sound (m/s):  v = t*0.6 + 331.4

Where t = temperature (°C)

Fundamental Resonant Frequencies in an Open Pipe:  fn = v/(2*L)

Where fn = frequency (Hz), v = speed of sound (m/s), L = length of pipe (m)

Program:

Partitions allowed:  1-5

STEP	CODE	KEY	COMMENT
00	65	*
01	93	.	Decimal point
02	06	6
03	85	+
04	03	3
05	03	3
06	01	1
07	93	.	Decimal point
08	04	4
09	95	=
10	12	R/S	Display speed of sound
11	55	÷
12	02	2
13	55	÷
14	12	R/S	Prompt for L
15	95	=
16	12	R/S	Display frequency

Speed of Sound in Dry Air: 

Input:  Enter temperature in °C [F1]

Result:  Speed of sound (m/s), press [R/S]

Fundamental Resonant Frequencies:

Store the length of the open pipe (m) then press [R/S]

Result:  Fundamental Resonant Frequency (Hz)

Test:

Open pipe of 0.45, where the temperature of the air is 39°C (102.2°F). 

Input:  39 [R/S]

Result:  354.8 m/s (speed of sound), [R/S]

394.22222 Hz (fundamental resonant frequency)

Source:  Browne Ph. D, Michael.  “Schaum’s Outlines:  Physics for Engineering and Science”  2^nd Ed.  McGraw Hill: New York, 2010

 Eddie

I hope you are enjoying this series of programs for calculators from the 1980s.  The next series, I plan to stay in the 1980s when I work with the 1988 HP 42S.

This blog is property of Edward Shore.