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  1. Newsgroups: comp.sources.hp48
  2. Path: sparky!uunet!seq!spell
  3. From: Mike Morgan <m00012@KANGA.STCLOUD.MSUS.EDU>
  4. Subject:  v06i022:  rlc_mm - RLC Form and Function Finder v1.0, Part01/01
  5. Message-ID: <1992Aug17.034649.15410@seq.uncwil.edu>
  6. Followup-To: comp.sys.hp48
  7. Sender: spell@seq.uncwil.edu (Chris Spell)
  8. Organization: Univ. of North Carolina @ Wilmington
  9. Date: Mon, 17 Aug 1992 03:46:49 GMT
  10. Approved: spell@seq.uncwil.edu
  11. Lines: 955
  12.  
  13. Checksum: 1371419103 (verify with brik -cv)
  14. Submitted-by: Mike Morgan <m00012@KANGA.STCLOUD.MSUS.EDU>
  15. Posting-number: Volume 6, Issue 22
  16. Archive-name: rlc_mm/part01
  17.  
  18. BEGIN_DOC rlc.doc
  19.  
  20. **************************
  21. *                        *
  22. *       FORM &           *
  23. * RLC             FINDER *   Version: Last
  24. *       FUNCTION         *
  25. *                        *
  26. * By:  Mike Morgan       *
  27. **************************
  28.  
  29. Credit is due to Dr. B. W. Ellis, Chairperson, Department of
  30. Electrical Engineering, College of Science and Technology,
  31. St. Cloud State University, St. Cloud, Minnesota.  He taught
  32. the Circuit Analysis course I took before I wrote this
  33. program.  He is an excellent teacher--but he would probably
  34. frown upon anybody using this program during exams.
  35.  
  36. Also, "ENGINEERING CIRCUIT ANALYSIS" by William H. Hayt, Jr.,
  37. and Jack E. Kemmerly, chapter 7, pp. 194-228 of the Fourth
  38. Edition was used as a reference.  This is the text many
  39. students must use while taking their first courses in
  40. Circuit Analysis, and this program helps solve the problems
  41. for chapter 7.  These problems are difficult, and it is
  42. easy to make dumb mistakes.
  43.  
  44. My program is best suited for checking your homework and
  45. learning the method of solving these problems.  Also, please
  46. note that these programs work *ONLY* on problems like those
  47. found in chapter 7 of the above-cited text, i.e., simple
  48. RLC circuit responses in the time domain.
  49.  
  50. DESCRIPTION:
  51.  
  52. This program finds a time domain response of a simple RLC
  53. circuit. The response is either given explicitly or in
  54. general terms with arbitrary contsants.  It prompts the user
  55. for the required parameters.  Form Finder finds the general
  56. form with arbitrary constants and Function Finder finds the
  57. explicit form of a response.
  58.  
  59. This version is completely free and may be distributed,
  60. modified, etc., so long as my name is attached to the
  61. program in some way.  Also, I assume absolutely no
  62. responsibility for any damages whatsoever.  Use these
  63. programs at your own risk!!!
  64.  
  65. INSTRUCTIONS:
  66.  
  67. Download the programs, contained in a directory, as 'RLC'.
  68. If you are using the version already in user RPL, you must
  69. run the 'SETUP' program, which deletes itself, to get the
  70. main program ready for running.  If you download the ASC
  71. version, there is no need for this.
  72.  
  73. To run the programs, hit the 'RUNIT' menu key.  You will
  74. then be presented with a menu screen.  Choose either Form
  75. Finder or Funtion Finder by toggling between the two with
  76. the up or down arrow, and hitting ENTER when the arrow on
  77. the menu screen points to the program you want to run.  The
  78. program then prompts the user for the required parmaters.
  79. It is self explanitory from there.
  80.  
  81. HINTS:
  82.  
  83. One helpful feature, which may be obvious, is that when the
  84. program requests the resistance, for example, and you want
  85. to enter a 5 Ohm in parallel with a 15 Ohm, you may enter
  86. the resistance as follows:
  87.  
  88.      5 INV 15 INV + INV <ENTER>
  89.  
  90. where INV is obtained by hitting the '1/X' key.
  91.  
  92. One bug is that you may not have any variables with the name
  93. 'A1' or 'A2' in any directory under the 'RLC' directory
  94. without the possibility of obtaining incorrect answers.  So,
  95. don't name anything A1 or A2.
  96.  
  97. This program saves the system and user flags and restores
  98. them upon completion.  Interupt the program during execution
  99. at the risk of screwing up your flag settings.
  100.  
  101. EXAMPLES:
  102.  
  103. Consider the following circuit:
  104.  
  105.               Is
  106.              _____
  107.             (     )      R1
  108.      ------(  <--  )----/\/\/\---
  109.      !      (_____)              !
  110.      !                           !
  111.      !               \/          !
  112.      !               /\ @t=0     !
  113.      !______________/ \/  _______!_______________
  114.      !                           !               !
  115.      !                           !               !
  116.      !                          _!_ +            /
  117.      (                        C ___  Vc(t)       \ R2
  118.   L  )                           !  -            /
  119.      (                           !               !
  120.      !___________________________!_______________!
  121.  
  122. Where:  After being open for a long time, the switch closes
  123.         at time t=0 seconds, and
  124.  
  125.           Is = 15 Amps
  126.            L =  0.5 Heneries
  127.            C =  1/32 Farads
  128.           R1 = 50 Ohms
  129.           R2 = 2 Ohms
  130.        Vc(t) = desired response
  131.  
  132. Run Form Finder.
  133.  
  134. Enter the RLC directory, and hit the menu key marked
  135. 'RUNIT'.  Using the up and down arrow keys, chose Form
  136. Finder and hit ENTER.  The program will prompt for the
  137. resistance.  (Sorry if I'm explaining too much...)  Since
  138. the 50 Ohm resistor is effectively cut out of the circuit
  139. for time t >= 0 seconds, the only resistance is the 2 Ohm
  140. resistor.  Hit 2 and then hit enter.  For the inductance
  141. enter 0.5.  For the Capacitance, use the following key
  142. strokes:  32 INV ENTER.  Then you will be prompted for
  143. series or parallel.  Hit the menu key marked '(P)' for
  144. parallel.
  145.  
  146. After a brief period, the stack will contain the following
  147. data:
  148.  
  149.         6:  ( greek alpha): 8
  150.         5: ( greek omega0): 8
  151.         4: d/dt(f(t))|t=0+: 'A1-8*A2'
  152.         3:       f(t)|t=0+: 'A2'
  153.         2:        function: 'e^-(8*t)*(A1*t+A2)'
  154.         1:  "Critically Damped"
  155.  
  156. This information represents, I hope, the major steps
  157. required to solve such a problem.  Consequently, it would
  158. be helpful if this program were used during an exam...if,
  159. of course, your professor allows it.
  160.  
  161. Now run Function Finder for the same circuit.  Enter the
  162. resistance, inductance and capacitance as before.  You will
  163. then be prompted for the forced part of the responce you
  164. desire.  The 15 Amp source will be isolated after the
  165. switch closes, so there is no forcing function.  Therefore,
  166. enter 0.  Next, you will be prompted for the initial value.
  167. For this circuit, we want the voltage accross the capacitor,
  168. plus to minus--top to bottom.  The entire 15 amps will flow
  169. through the inductor ( a short to DC ), bypass the capacitor
  170. ( open circuit to DC), and through the resistor before the
  171. switch closes  (Remember, capacitor voltages must be
  172. continuous.)  Consequently, the resistor will have a voltage
  173. of 15 Amps times 2 Ohms sensed positively at the bottom of
  174. the resistor by the passive sign convention and Ohm's law.
  175. The capacitor is in parallel with the resistor, so it will
  176. have an equal voltage immediately before, and consequently
  177. after, the switch closes.  However, this initial voltage
  178. *must* be entered as a negative value because the desired
  179. response is plus to minus--TOP to BOTTOM and the resistor
  180. voltage is plus to minus--BOTTOM to TOP.  So enter the
  181. initial value with:  15 2 * NEG ENTER.  Now you are prompted
  182. for the initial deriviative (two hints are given).  For a
  183. capacitor, dv/dt=i/C.  The current through the inductor must
  184. be continous, and so the 15 Amps flowing through the
  185. inductor must go through the resistor to keep the capacitor
  186. voltage constant.   As a result, no current is passing
  187. through the capacitor immediately after the switch closes,
  188. so dv/dt=0/1/32=0*32=0.  Therefore, enter 0.  Finally, hit
  189. the menu key marked '(P)' for parallel.
  190.  
  191. After a brief period, the stack will contain:
  192.  
  193. 1:  'e^-(8*t)*(-(240*t)-30)'
  194.  
  195. Which is Vc(t).
  196.  
  197. This function may then be plotted using the plotter
  198. application and setting the independant variable to 't'.
  199.  
  200. Excuse my poor example, I am not a good teacher...but I hope
  201. it is helpful anyway.  (One thing is sure:  you still need
  202. to know the concepts invlolved to use the Function Finder
  203. program!)
  204.  
  205. HOW IT WORKS:
  206.  
  207. Let
  208.    R=Resistance*
  209.    L=Inductance*
  210.    C=Capacitance*
  211.    a=exponential damping coefficiant (neper frequency)
  212.   w0=resonant radian frequency
  213.   wd=natural resonant frequency
  214.   S1=(first) complex frequency
  215.   S2=(second) complex frequency
  216.   A1=(first) arbitrary constant
  217.   A2=(second) arbitrary constant
  218.   fi=response funtion's initial value*
  219.   fp=value function approaches as time approaches infinity*
  220.   id=initial value of function's derivative*
  221.  
  222. * means value is supplied by user.
  223.  
  224. The program calculates:
  225.  
  226.         a=1/(2*R*C)        if circuit is in parallel
  227.         a=R/(2*L)          if circuit is in series
  228.  
  229.         w0=1/SQRT(L*C)
  230.  
  231. Now, the response of a simple RLC circuit has three forms,
  232. depending on the relative values of 'a' and 'w0'
  233.  
  234.  
  235. If 'a' is greater than 'w0', the response is *overdamped*,
  236. and it has the form:
  237.  
  238.         f(t)=A1*e^(S1*t)+A2*e^(S2*t)+fp (1)
  239.  
  240. Where S1 and S2 are calculated with:
  241.  
  242.         S1=-a+SQRT(a^2-w0^2) if a > w0
  243.         S2=-a-SQRT(a^2-w0^2) if a > w0
  244.  
  245. and A1 and A2 are arbitrary constants.
  246.  
  247. At t=0, f(0)=fi=A1+A2+fp ==> A1+A2=fi-fp (2)
  248.  
  249. Where 'fi' and 'fp' are supplied by the user.  Taking the
  250. derivative of (1) and evaluating it at t=0, you get:
  251.  
  252. f'(t)=S1*A1*e^(S1*t)+S2*A2*e^(S2*t)
  253. f'(0)=id=S1*A1+S2*A2 (3)
  254.  
  255. Where, again, 'id' is supplied by the user.  Because the
  256. program has already calculated 'S1' and 'S2', (2) and (3)
  257. constitute two linear equations with two unknowns:
  258.  
  259.                    A1 +    A2 = fi-fp (2)
  260.                 S1*A1 + S2*A2 = id    (3)
  261.  
  262. 'A1' and 'A2' can be found with matrices on the HP 48SX:
  263.  
  264.  [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  1  1 ]
  265.    [ A2 ] ]     [    id     ] ]  /       S1 S2 ] ]
  266.  
  267. (Note:  No hate mail from mathematicians, please.)
  268.  
  269. If 'a' is equal to 'w0', then the response is *critically
  270. damped*, the response is in the form:
  271.  
  272.         f(t)=e^(-a*t)*(A1*t+A2)+fp
  273.  
  274. Where 'A1' and 'A2 are given by:
  275.  
  276.  [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  0  1 ]
  277.    [ A2 ] ]     [    id     ] ]  /        1 -a ] ]
  278.  
  279. If 'a' is less than 'w0', then the response is *under
  280. damped*, and is in the form:
  281.  
  282.         f(t)=e(-a*t)*(A1*COS(wd*t)+A2*SIN(wd*t))+fp
  283.  
  284. Where:
  285.  
  286.         wd=SQRT(w0^2-a&^2) if w0 > a
  287.  
  288. And, where 'A1' and 'A2' are given by:
  289.  
  290.  [ [ A1 ]   = [ [ (fi - fp) ]     /  [ [  1  0 ]
  291.    [ A2 ] ]     [    id     ] ]  /       -a wd ] ]
  292.  
  293. Thank you,
  294.  
  295. Mike Morgan
  296. email:  M00012@KANGA.STCLOUD.MSUS.EDU
  297.         mmorgan@solar.stcloud.msus.edu
  298.  
  299. mail:   K.H.K.
  300.         428 7th Ave. S.
  301.         St. Cloud, MN 56301
  302.         (612) 654-6010
  303.  
  304. END_DOC
  305.  
  306.  
  307. BEGIN_RPL rlc.rpl
  308. %%HP: T(3)A(R)F(.);
  309. DIR
  310.   SETUP
  311.     \<< Subs RLCP
  312. OBJ\-> DROP 1 68
  313.       FOR X +
  314.       NEXT OBJ\->
  315. 'RLCP' STO RLCL
  316. OBJ\-> DROP 1 3
  317.       FOR X +
  318.       NEXT OBJ\->
  319. 'RLCL' STO ERASE {
  320. # 0h # 0h } PVIEW
  321. PICT { # 0h # 0h }
  322. RLCP GXOR 1 WAIT 1
  323. 3
  324.       FOR Y PICT {
  325. # 1Ah # 20h } RLCL
  326. GXOR .3 WAIT 1 5
  327.         FOR X 30
  328. .05 BEEP 40 .05
  329. BEEP
  330.         NEXT PICT {
  331. # 1Ah # 20h } RLCL
  332. GXOR
  333.       NEXT 5 WAIT
  334. UPDIR 'SETUP' PURGE
  335.     \>>
  336.   RUNIT
  337.     \<< Subs ERASE {
  338. # 0h # 0h } PVIEW
  339. PICT { # 0h # 0h }
  340. RLCP GXOR RCLF
  341. 'OFL' STO {
  342. # 40000000810FF0h
  343. # 0h } STOF { # 23h
  344. # 3h } { # 23h # 9h
  345. } 0 \-> p1 p2 dy
  346.       \<< PICT p1 ARR
  347. GXOR
  348.         WHILE dy
  349. NOT
  350.         REPEAT 0
  351. WAIT IP \-> key
  352.           \<<
  353.             IF key
  354. 51 ==
  355.             THEN 1
  356. 'dy' STO
  357.             ELSE
  358.               IF
  359. key 25 == key 35 ==
  360. OR
  361.               THEN
  362. IF 3 FS?
  363. THEN PICT p1 ARR
  364. GXOR PICT p2 ARR
  365. GXOR 3 CF
  366. ELSE PICT p2 ARR
  367. GXOR PICT p1 ARR
  368. GXOR 3 SF
  369. END
  370.               END
  371.             END
  372.           \>>
  373.         END
  374.       \>> PICT {
  375. # 1Ah # 20h } RLCL
  376. GXOR .3 WAIT PICT {
  377. # 1Ah # 20h } RLCL
  378. GXOR .5 WAIT
  379.       IF 3 FC?C
  380.       THEN FRMFD
  381.       ELSE FNCFD
  382.       END OFL STOF
  383. UPDIR
  384.     \>>
  385.   Subs
  386.     DIR
  387.       FRMFD
  388.         \<< GRAV GIAV
  389. GCAV SOSOP CCFF
  390.         \>>
  391.       FNCFD
  392.         \<< GRAV GIAV
  393. GCAV GFP GIV GID
  394. SOSOP CCFN
  395.         \>>
  396.       RLCP {
  397. "GROB 131 64 "
  398. "DFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
  399. "50400000000000000000000000000000"
  400. "00107000000000000000000000000000"
  401. "00007010000000000773111000000000"
  402. "0000004010000000000155B920000000"
  403. "00000000401000F40E00075351B000F9"
  404. "31D1FD30004010001501100155194000"
  405. "101152144000401000150100017511B0"
  406. "00101354144000401000F40100000000"
  407. "0000F01554FC30004010005401000759"
  408. "CEAB4010195414100040100094011001"
  409. "5B24AA501011521420004010001D7E00"
  410. "075F24AA701831D1F540004010000000"
  411. "00015D24AA6000000000000040100000"
  412. "00000179C4AB40000000000000401000"
  413. "00000000000000000000000000004010"
  414. "070F1000000000000000000000000040"
  415. "10E8F060081000808004000000000000"
  416. "4018140181746000CD5D120000000000"
  417. "00401408020A82810080416100000000"
  418. "000040120000060102008C5180000000"
  419. "00000040110000018001008180E00000"
  420. "00000000401100008000020000001100"
  421. "00000000004090000080000400000845"
  422. "00000000000040900000000004000006"
  423. "83300000000000409020666500040FFF"
  424. "F701FFFFFFFFFFF14017201115008201"
  425. "00060030200040000140941021250201"
  426. "01000000002000400001409800414501"
  427. "02010000000020004000014019003637"
  428. "0202C700000000200040000140150000"
  429. "00044138100000081000200001409000"
  430. "000408B8012000000700001000014098"
  431. "000064E7040140000008F008E0000140"
  432. "9110009A1004C7400000000708130001"
  433. "401A00289100A20180000038F04CE006"
  434. "01401400280000A20180000057004813"
  435. "09EF401810140000A20080600038F04C"
  436. "E001004010E8230000420080A0005007"
  437. "481309EF401007C00000420080600058"
  438. "F0CDE0060140100000000004C740A000"
  439. "070008130001401000000000040040A0"
  440. "0008F008E00001401000000000080020"
  441. "00000007001000014010000000000038"
  442. "10111000C00020000140100000000000"
  443. "C7001110002000400001401000000000"
  444. "00010011100020004000014010000000"
  445. "00000108AA2000200040000140100000"
  446. "0000000108AA20002000400001401000"
  447. "000000000FF7AA2FFFFFFFFFFFF14010"
  448. "00000000000000AAA000000000000040"
  449. "1000000000000000AAA0000000000000"
  450. "40100000000000000044400000000000"
  451. "00401000000000000000444000000000"
  452. "000040100000000000000044400000E1"
  453. "00000040100000000000000000000000"
  454. "12000000409700001111000110000000"
  455. "08C4807C1740980030B101000B100000"
  456. "000429C882A8409822305919830593D9"
  457. "3EC30428888228409722005115440554"
  458. "344054042880FC36409822301113C701"
  459. "54144E5404298080214098C330111540"
  460. "015418715408C4804090409702001939"
  461. "830193104E540012C13C8F4010C10000"
  462. "0000000008300000E100000040700000"
  463. "00000000000000000000000000704000"
  464. "000000000000000000000000000010DF"
  465. "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF50"
  466. }
  467.       RLCL {
  468. "GROB 15 21 "
  469. "0040002010201F40F840084004200420"
  470. "0493047202010A3106A000A000700050"
  471. "00300030081008100800"
  472. }
  473.       ARR
  474. GROB 7 5 0102F70201
  475.       GET1
  476.         \<< { "" V }
  477. INPUT OBJ\->
  478.         \>>
  479.       GRAV
  480.         \<<
  481. "Enter Resistance"
  482. GET1
  483.           WHILE DUP
  484. 0 \<=
  485.           REPEAT
  486. DROP
  487. "Resistance > 0"
  488. GET1
  489.           END
  490.         \>>
  491.       GIAV
  492.         \<<
  493. "Enter Inductance"
  494. GET1
  495.           WHILE DUP
  496. 0 \<=
  497.           REPEAT
  498. DROP
  499. "Inductance > 0"
  500. GET1
  501.           END
  502.         \>>
  503.       GCAV
  504.         \<<
  505. "Enter Capacitance"
  506. GET1
  507.           WHILE DUP
  508. 0 \<=
  509.           REPEAT
  510. DROP
  511. "Capacitance > 0"
  512. GET1
  513.           END
  514.         \>>
  515.       GFP
  516.         \<<
  517. "Enter Forced Part"
  518. GET1
  519.         \>>
  520.       GIV
  521.         \<<
  522. "Enter Initial Value"
  523. GET1
  524.         \>>
  525.       GID
  526.         \<<
  527. "Enter Initial Deriv.
  528.  di/dt=v/L
  529.  dv/dt=i/C"
  530. GET1
  531.         \>>
  532.       SOSOP
  533.         \<< CLLCD
  534. "Series or Parallel?"
  535. 1 DISP
  536. "(S)  series  RLC"
  537. 3 DISP
  538. "(P) parallel RLC"
  539. 4 DISP { "(S)" ""
  540. "" "" "" "(P)" }
  541. TMENU
  542.           DO -1
  543. WAIT
  544.           UNTIL DUP
  545. DUP 11.1 == SWAP
  546. 16.1 == OR
  547.             IF
  548.             THEN 1
  549.             ELSE
  550. DROP 0
  551.             END
  552.           END
  553.           IF 11.1
  554. ==
  555.           THEN 1 CF
  556.           ELSE 1 SF
  557.           END 0
  558. MENU
  559.         \>>
  560.       CCFF
  561.         \<< CLLCD
  562. "Calculating" 4
  563. DISP \-> r l c
  564.           \<< r l c
  565. CA l c COMEGA0 \-> \Ga
  566. \Gw0
  567.             \<< \Ga "\Ga"
  568. \->TAG \Gw0 "\Gw0" \->TAG
  569.               IF \Ga
  570. \Gw0 >
  571.               THEN
  572. \Ga \Gw0 CS1S2 \-> s1 s2
  573. \<< s1 "S1" \->TAG s2
  574. "S2" \->TAG 's1*A1+s2
  575. *A2' EVAL
  576. "\.d/\.dt\166t=0+" \->TAG '
  577. A1+A2' "f\166t=0+"
  578. \->TAG 'A1*e^(s1*t)+
  579. A2*e^(s2*t)' EVAL
  580. "function" \->TAG
  581. \>> "Overdamped"
  582.               ELSE
  583. IF \Ga \Gw0 <
  584. THEN \Ga \Gw0 C\Gwd \-> \Gwd
  585.   \<< \Gwd "\Gwd" \->TAG '-
  586. \Ga*A1+\Gwd*A2' EVAL
  587. "\.d/\.dt\166t=0+" \->TAG
  588. 'A1' "f\166t=0+" \->TAG
  589. 'e^(-\Ga*t)*(A1*COS(
  590. \Gwd*t)+A2*SIN(\Gwd*t))
  591. ' EVAL "function"
  592. \->TAG
  593.   \>> "Underdamped"
  594. ELSE 'A1-\Ga*A2' EVAL
  595. "\.d/\.dt\166t=0+" \->TAG
  596. 'A2' "f\166t=0+" \->TAG
  597. 'e^(-\Ga*t)*(A1*t+A2)
  598. ' EVAL "function"
  599. \->TAG
  600. "Critically Damped"
  601. END
  602.               END
  603.             \>>
  604.           \>> 1 CF
  605.         \>>
  606.       CA
  607.         \<< \-> r l c
  608.           \<<
  609.             IF 1
  610. FS?
  611.             THEN 2
  612. r c * * INV
  613.             ELSE r
  614. 2 l * /
  615.             END
  616.           \>>
  617.         \>>
  618.       COMEGA0
  619.         \<< \-> l c
  620.           \<< l c * \v/
  621. INV
  622.           \>>
  623.         \>>
  624.       CS1S2
  625.         \<< \-> \Ga \Gw0
  626.           \<< \Ga 2 ^
  627. \Gw0 2 ^ - \v/ \-> r
  628.             \<< \Ga NEG
  629. r + \Ga NEG r -
  630.             \>>
  631.           \>>
  632.         \>>
  633.       C\Gwd
  634.         \<< \-> \Ga \Gw0
  635.           \<< \Gw0 2 ^
  636. \Ga 2 ^ - \v/
  637.           \>>
  638.         \>>
  639.       CCFN
  640.         \<< CLLCD
  641. "Calculating" 4
  642. DISP \-> r l c fp fi
  643. id
  644.           \<< r l c
  645. CA l c COMEGA0 \-> \Ga
  646. \Gw0
  647.             \<<
  648.               IF \Ga
  649. \Gw0 >
  650.               THEN
  651. \Ga \Gw0 CS1S2 \-> s1 s2
  652. \<< fi fp - id { 2 1
  653. } \->ARRY 1 1 s1 s2 {
  654. 2 2 } \->ARRY / OBJ\->
  655. DROP \-> A1 A2
  656.   \<< 'A1*e^(s1*t)+A2
  657. *e^(s2*t)+fp' EVAL
  658.   \>>
  659. \>>
  660.               ELSE
  661. IF \Ga \Gw0 <
  662. THEN \Ga \Gw0 C\Gwd \-> \Gwd
  663.   \<< fi fp - id { 2
  664. 1 } \->ARRY 1 0 \Ga NEG
  665. \Gwd { 2 2 } \->ARRY /
  666. OBJ\-> DROP \-> A1 A2
  667.     \<< 'e^(-\Ga*t)*(A1
  668. *COS(\Gwd*t)+A2*SIN(
  669. \Gwd*t))+fp' EVAL
  670.     \>>
  671.   \>>
  672. ELSE fi fp - id { 2
  673. 1 } \->ARRY 0 1 1 \Ga
  674. NEG { 2 2 } \->ARRY /
  675. OBJ\-> DROP \-> A1 A2
  676.   \<< 'e^(-\Ga*t)*(A1*t
  677. +A2)+fp' EVAL
  678.   \>>
  679. END
  680.               END
  681.             \>>
  682.           \>> 1 CF
  683.         \>>
  684.     END
  685.   dtag
  686.     \<< DTAG
  687.     \>>
  688.   up
  689.     \<< UPDIR
  690.     \>>
  691. END
  692.  
  693. END_RPL
  694.  
  695.  
  696. BEGIN_ASC rlc.asc
  697. %%HP: T(1);
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  961. sum -r/size 49093/6544 section (from "begin" to "end")
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  964.