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.  

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