Wednesday, July 6, 2016

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

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:  [2nd] [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”  2nd 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.