I'd be better at ____ than Tom

[buffcoat]

Golf, natch.

[dave from knoxville]

Solving Bernoulli equations

what is a bernoulli equation? Like the binomial distribution or is it more like a bessel function or what? Will you put it here?

For example, y prime minus y equals e to the x times y squared. Dividing each term by y squared produces the equation y to the negative two times y prime minus y to the negative one equals e to the x. In this form of the equation, we can let v equal y to the negative one, which implies that v prime equals negative y to the negative two times y prime. Shifting the negative in this expression to the left side of the equation gives negative v prime equals positive y to the negative two power times y prime. Now we can substitute these expressions for y to the negative one power and y to the negative two power times y prime into the transformed equation y to the negative two times y prime minus y to the negative one equals e to the x, producing the simpler negative v prime minus v equals e to the x. But this is a first order linear equation. Multiplying each term by negative one converts this equation to standard form v prime plus v equals negative e to the x. This type of first order linear differential equation is typically solved with a simple integrating factor of the form u of x equals e to the integral of p of x dx where p of x is the coefficient of the dependent variable, which, in this case, is just the constant one. So the integrating factor is simply e to the x. Multiplying this expression into each side of the current form of the differential equation produces e to the x times v prime plus e to the x times v equals negative e to the two x. According to standard procedure, the sum on the left side of this equation represents the derivative with respect to x of the product e to the x times v. Integrating each side of the equation with respect to x produces an equation that is free of all derivatives. That equation is e to the x times v equals c minus one half of e to the two x, where c is an arbitrary constant. Replacing v with one over y, e to the x over y equals c minus one half of e to the two x. Multiplying y to the right of the equation, dividing c minus one half of e to the two x to the left, and doubling the denominator and numerator so as to resolve the resulting complex fraction produces y equals two times e to the x divided by ( c minus e to the two x).

Let me know if you find a mistake in this.

[erika]

My brain is bleeding.

[Wes]

Solving Bernoulli Bore-noulli equations

what is a bernoulli equation? Like the binomial distribution or is it more like a bessel function or what? Will you put it here?

For example, y prime minus y equals e to the x times y squared. Dividing each term by y squared produces the equation y to the negative two times y prime minus y to the negative one equals e to the x. In this form of the equation, we can let v equal y to the negative one, which implies that v prime equals negative y to the negative two times y prime. Shifting the negative in this expression to the left side of the equation gives negative v prime equals positive y to the negative two power times y prime. Now we can substitute these expressions for y to the negative one power and y to the negative two power times y prime into the transformed equation y to the negative two times y prime minus y to the negative one equals e to the x, producing the simpler negative v prime minus v equals e to the x. But this is a first order linear equation. Multiplying each term by negative one converts this equation to standard form v prime plus v equals negative e to the x. This type of first order linear differential equation is typically solved with a simple integrating factor of the form u of x equals e to the integral of p of x dx where p of x is the coefficient of the dependent variable, which, in this case, is just the constant one. So the integrating factor is simply e to the x. Multiplying this expression into each side of the current form of the differential equation produces e to the x times v prime plus e to the x times v equals negative e to the two x. According to standard procedure, the sum on the left side of this equation represents the derivative with respect to x of the product e to the x times v. Integrating each side of the equation with respect to x produces an equation that is free of all derivatives. That equation is e to the x times v equals c minus one half of e to the two x, where c is an arbitrary constant. Replacing v with one over y, e to the x over y equals c minus one half of e to the two x. Multiplying y to the right of the equation, dividing c minus one half of e to the two x to the left, and doubling the denominator and numerator so as to resolve the resulting complex fraction produces y equals two times e to the x divided by ( c minus e to the two x).

Let me know if you find a mistake in this.

Fixed!

[dave from knoxville]

Solving Bernoulli Bore-noulli equations

what is a bernoulli equation? Like the binomial distribution or is it more like a bessel function or what? Will you put it here?

For example, y prime minus y equals e to the x times y squared. Dividing each term by y squared produces the equation y to the negative two times y prime minus y to the negative one equals e to the x. In this form of the equation, we can let v equal y to the negative one, which implies that v prime equals negative y to the negative two times y prime. Shifting the negative in this expression to the left side of the equation gives negative v prime equals positive y to the negative two power times y prime. Now we can substitute these expressions for y to the negative one power and y to the negative two power times y prime into the transformed equation y to the negative two times y prime minus y to the negative one equals e to the x, producing the simpler negative v prime minus v equals e to the x. But this is a first order linear equation. Multiplying each term by negative one converts this equation to standard form v prime plus v equals negative e to the x. This type of first order linear differential equation is typically solved with a simple integrating factor of the form u of x equals e to the integral of p of x dx where p of x is the coefficient of the dependent variable, which, in this case, is just the constant one. So the integrating factor is simply e to the x. Multiplying this expression into each side of the current form of the differential equation produces e to the x times v prime plus e to the x times v equals negative e to the two x. According to standard procedure, the sum on the left side of this equation represents the derivative with respect to x of the product e to the x times v. Integrating each side of the equation with respect to x produces an equation that is free of all derivatives. That equation is e to the x times v equals c minus one half of e to the two x, where c is an arbitrary constant. Replacing v with one over y, e to the x over y equals c minus one half of e to the two x. Multiplying y to the right of the equation, dividing c minus one half of e to the two x to the left, and doubling the denominator and numerator so as to resolve the resulting complex fraction produces y equals two times e to the x divided by ( c minus e to the two x).

Let me know if you find a mistake in this.

Fixed!

I did just work out the confirmation, if you want me to type it up, but it's a little more involved than the solution, so I would need some advance warning...

[Julie]

Solving Bernoulli equations

what is a bernoulli equation? Like the binomial distribution or is it more like a bessel function or what? Will you put it here?

For example, y prime minus y equals e to the x times y squared. Dividing each term by y squared produces the equation y to the negative two times y prime minus y to the negative one equals e to the x. In this form of the equation, we can let v equal y to the negative one, which implies that v prime equals negative y to the negative two times y prime. Shifting the negative in this expression to the left side of the equation gives negative v prime equals positive y to the negative two power times y prime. Now we can substitute these expressions for y to the negative one power and y to the negative two power times y prime into the transformed equation y to the negative two times y prime minus y to the negative one equals e to the x, producing the simpler negative v prime minus v equals e to the x. But this is a first order linear equation. Multiplying each term by negative one converts this equation to standard form v prime plus v equals negative e to the x. This type of first order linear differential equation is typically solved with a simple integrating factor of the form u of x equals e to the integral of p of x dx where p of x is the coefficient of the dependent variable, which, in this case, is just the constant one. So the integrating factor is simply e to the x. Multiplying this expression into each side of the current form of the differential equation produces e to the x times v prime plus e to the x times v equals negative e to the two x. According to standard procedure, the sum on the left side of this equation represents the derivative with respect to x of the product e to the x times v. Integrating each side of the equation with respect to x produces an equation that is free of all derivatives. That equation is e to the x times v equals c minus one half of e to the two x, where c is an arbitrary constant. Replacing v with one over y, e to the x over y equals c minus one half of e to the two x. Multiplying y to the right of the equation, dividing c minus one half of e to the two x to the left, and doubling the denominator and numerator so as to resolve the resulting complex fraction produces y equals two times e to the x divided by ( c minus e to the two x).

Let me know if you find a mistake in this.

I do not know this, so I will not find a mistake. But instead of providing a proof in english word, could you just, as a very special favor, put the equations?

y=(2e^x)/(c-e^2x)

because my main problem is word understanding. But I certainly understand the symbols and such.

[Andy]

here you go
t   Xa   Ya   Xb   Yb   D
223   1091.61016   958.000699   1091.110334   957.9436095   0.503075033
1   4.9   1756.4   204   4.3   1763.376086
2   9.8   1752.8   208   8.6   1755.424986
3   14.7   1749.2   212   12.9   1747.473885
4   19.6   1745.6   216   17.2   1739.522785
5   24.5   1742   220   21.5   1731.571685
6   29.4   1738.4   224   25.8   1723.620585
7   34.3   1734.8   228   30.1   1715.669484
8   39.2   1731.2   232   34.4   1707.718384
9   44.1   1727.6   236   38.7   1699.767284
10   49   1724   240   43   1691.816184
11   53.9   1720.4   244   47.3   1683.865084
12   58.8   1716.8   248   51.6   1675.913983
13   63.7   1713.2   252   55.9   1667.962883
14   68.6   1709.6   256   60.2   1660.011783
15   73.5   1706   260   64.5   1652.060683
16   78.4   1702.4   264   68.8   1644.109583
17   83.3   1698.8   268   73.1   1636.158483
18   88.2   1695.2   272   77.4   1628.207382
19   93.1   1691.6   276   81.7   1620.256282
20   98   1688   280   86   1612.305182
21   102.9   1684.4   284   90.3   1604.354082
22   107.8   1680.8   288   94.6   1596.402982
23   112.7   1677.2   292   98.9   1588.451882
24   117.6   1673.6   296   103.2   1580.500781
25   122.5   1670   300   107.5   1572.549681
26   127.4   1666.4   304   111.8   1564.598581
27   132.3   1662.8   308   116.1   1556.647481
28   137.2   1659.2   312   120.4   1548.696381
29   142.1   1655.6   316   124.7   1540.745281
30   147   1652   320   129   1532.794181
31   151.9   1648.4   324   133.3   1524.84308
32   156.8   1644.8   328   137.6   1516.89198
33   161.7   1641.2   332   141.9   1508.94088
34   166.6   1637.6   336   146.2   1500.98978
35   171.5   1634   340   150.5   1493.03868
36   176.4   1630.4   344   154.8   1485.08758
37   181.3   1626.8   348   159.1   1477.13648
38   186.2   1623.2   352   163.4   1469.18538
39   191.1   1619.6   356   167.7   1461.23428
40   196   1616   360   172   1453.28318
41   200.9   1612.4   364   176.3   1445.332079
42   205.8   1608.8   368   180.6   1437.380979
43   210.7   1605.2   372   184.9   1429.429879
44   215.6   1601.6   376   189.2   1421.478779
45   220.5   1598   380   193.5   1413.527679
46   225.4   1594.4   384   197.8   1405.576579
47   230.3   1590.8   388   202.1   1397.625479
48   235.2   1587.2   392   206.4   1389.674379
49   240.1   1583.6   396   210.7   1381.723279
50   245   1580   400   215   1373.772179
51   249.9   1576.4   404   219.3   1365.821079
52   254.8   1572.8   408   223.6   1357.869979
53   259.7   1569.2   412   227.9   1349.918879
54   264.6   1565.6   416   232.2   1341.967779
55   269.5   1562   420   236.5   1334.016679
56   274.4   1558.4   424   240.8   1326.065579
57   279.3   1554.8   428   245.1   1318.114479
58   284.2   1551.2   432   249.4   1310.163379
59   289.1   1547.6   436   253.7   1302.212279
60   294   1544   440   258   1294.261179
61   298.9   1540.4   444   262.3   1286.310079
62   303.8   1536.8   448   266.6   1278.358979
63   308.7   1533.2   452   270.9   1270.407879
64   313.6   1529.6   456   275.2   1262.456779
65   318.5   1526   460   279.5   1254.50568
66   323.4   1522.4   464   283.8   1246.55458
67   328.3   1518.8   468   288.1   1238.60348
68   333.2   1515.2   472   292.4   1230.65238
69   338.1   1511.6   476   296.7   1222.70128
70   343   1508   480   301   1214.75018
71   347.9   1504.4   484   305.3   1206.79908
72   352.8   1500.8   488   309.6   1198.84798
73   357.7   1497.2   492   313.9   1190.896881
74   362.6   1493.6   496   318.2   1182.945781
75   367.5   1490   500   322.5   1174.994681
76   372.4   1486.4   504   326.8   1167.043581
77   377.3   1482.8   508   331.1   1159.092481
78   382.2   1479.2   512   335.4   1151.141381
79   387.1   1475.6   516   339.7   1143.190282
80   392   1472   520   344   1135.239182
81   396.9   1468.4   524   348.3   1127.288082
82   401.8   1464.8   528   352.6   1119.336982
83   406.7   1461.2   532   356.9   1111.385883
84   411.6   1457.6   536   361.2   1103.434783
85   416.5   1454   540   365.5   1095.483683
86   421.4   1450.4   544   369.8   1087.532583
87   426.3   1446.8   548   374.1   1079.581484
88   431.2   1443.2   552   378.4   1071.630384
89   436.1   1439.6   556   382.7   1063.679284
90   441   1436   560   387   1055.728185
91   445.9   1432.4   564   391.3   1047.777085
92   450.8   1428.8   568   395.6   1039.825985
93   455.7   1425.2   572   399.9   1031.874886
94   460.6   1421.6   576   404.2   1023.923786
95   465.5   1418   580   408.5   1015.972687
96   470.4   1414.4   584   412.8   1008.021587
97   475.3   1410.8   588   417.1   1000.070488
98   480.2   1407.2   592   421.4   992.119388
99   485.1   1403.6   596   425.7   984.1682885
100   490   1400   600   430   976.2171889
101   494.9   1396.4   604   434.3   968.2660895
102   499.8   1392.8   608   438.6   960.31499
103   504.7   1389.2   612   442.9   952.3638905
104   509.6   1385.6   616   447.2   944.4127911
105   514.5   1382   620   451.5   936.4616917
106   519.4   1378.4   624   455.8   928.5105923
107   524.3   1374.8   628   460.1   920.5594929
108   529.2   1371.2   632   464.4   912.6083936
109   534.1   1367.6   636   468.7   904.6572942
110   539   1364   640   473   896.7061949
111   543.9   1360.4   644   477.3   888.7550956
112   548.8   1356.8   648   481.6   880.8039964
113   553.7   1353.2   652   485.9   872.8528971
114   558.6   1349.6   656   490.2   864.9017979
115   563.5   1346   660   494.5   856.9506987
116   568.4   1342.4   664   498.8   848.9995995
117   573.3   1338.8   668   503.1   841.0485004
118   578.2   1335.2   672   507.4   833.0974013
119   583.1   1331.6   676   511.7   825.1463022
120   588   1328   680   516   817.1952031
121   592.9   1324.4   684   520.3   809.2441041
122   597.8   1320.8   688   524.6   801.2930051
123   602.7   1317.2   692   528.9   793.3419061
124   607.6   1313.6   696   533.2   785.3908072
125   612.5   1310   700   537.5   777.4397083
126   617.4   1306.4   704   541.8   769.4886094
127   622.3   1302.8   708   546.1   761.5375106
128   627.2   1299.2   712   550.4   753.5864118
129   632.1   1295.6   716   554.7   745.635313
130   637   1292   720   559   737.6842143
131   641.9   1288.4   724   563.3   729.7331156
132   646.8   1284.8   728   567.6   721.782017
133   651.7   1281.2   732   571.9   713.8309184
134   656.6   1277.6   736   576.2   705.8798198
135   661.5   1274   740   580.5   697.9287213
136   666.4   1270.4   744   584.8   689.9776228
137   671.3   1266.8   748   589.1   682.0265244
138   676.2   1263.2   752   593.4   674.075426
139   681.1   1259.6   756   597.7   666.1243277
140   686   1256   760   602   658.1732295
141   690.9   1252.4   764   606.3   650.2221313
142   695.8   1248.8   768   610.6   642.2710331
143   700.7   1245.2   772   614.9   634.319935
144   705.6   1241.6   776   619.2   626.368837
145   710.5   1238   780   623.5   618.4177391
146   715.4   1234.4   784   627.8   610.4666412
147   720.3   1230.8   788   632.1   602.5155434
148   725.2   1227.2   792   636.4   594.5644456
149   730.1   1223.6   796   640.7   586.613348
150   735   1220   800   645   578.6622504
151   739.9   1216.4   804   649.3   570.7111529
152   744.8   1212.8   808   653.6   562.7600554
153   749.7   1209.2   812   657.9   554.8089581
154   754.6   1205.6   816   662.2   546.8578609
155   759.5   1202   820   666.5   538.9067637
156   764.4   1198.4   824   670.8   530.9556667
157   769.3   1194.8   828   675.1   523.0045698
158   774.2   1191.2   832   679.4   515.053473
159   779.1   1187.6   836   683.7   507.1023763
160   784   1184   840   688   499.1512797
161   788.9   1180.4   844   692.3   491.2001832
162   793.8   1176.8   848   696.6   483.2490869
163   798.7   1173.2   852   700.9   475.2979907
164   803.6   1169.6   856   705.2   467.3468947
165   808.5   1166   860   709.5   459.3957988
166   813.4   1162.4   864   713.8   451.4447031
167   818.3   1158.8   868   718.1   443.4936076
168   823.2   1155.2   872   722.4   435.5425123
169   828.1   1151.6   876   726.7   427.5914171
170   833   1148   880   731   419.6403222
171   837.9   1144.4   884   735.3   411.6892275
172   842.8   1140.8   888   739.6   403.738133
173   847.7   1137.2   892   743.9   395.7870387
174   852.6   1133.6   896   748.2   387.8359447
175   857.5   1130   900   752.5   379.884851
176   862.4   1126.4   904   756.8   371.9337575
177   867.3   1122.8   908   761.1   363.9826644
178   872.2   1119.2   912   765.4   356.0315716
179   877.1   1115.6   916   769.7   348.0804792
180   882   1112   920   774   340.1293871
181   886.9   1108.4   924   778.3   332.1782955
182   891.8   1104.8   928   782.6   324.2272043
183   896.7   1101.2   932   786.9   316.2761135
184   901.6   1097.6   936   791.2   308.3250233
185   906.5   1094   940   795.5   300.3739336
186   911.4   1090.4   944   799.8   292.4228445
187   916.3   1086.8   948   804.1   284.4717561
188   921.2   1083.2   952   808.4   276.5206683
189   926.1   1079.6   956   812.7   268.5695813
190   931   1076   960   817   260.6184951
191   935.9   1072.4   964   821.3   252.6674098
192   940.8   1068.8   968   825.6   244.7163256
193   945.7   1065.2   972   829.9   236.7652424
194   950.6   1061.6   976   834.2   228.8141604
195   955.5   1058   980   838.5   220.8630798
196   960.4   1054.4   984   842.8   212.9120006
197   965.3   1050.8   988   847.1   204.9609231
198   970.2   1047.2   992   851.4   197.0098475
199   975.1   1043.6   996   855.7   189.0587739
200   980   1040   1000   860   181.1077028
201   984.9   1036.4   1004   864.3   173.1566343
202   989.8   1032.8   1008   868.6   165.2055689
203   994.7   1029.2   1012   872.9   157.2545071
204   999.6   1025.6   1016   877.2   149.3034494
205   1004.5   1022   1020   881.5   141.3523965
206   1009.4   1018.4   1024   885.8   133.4013493
207   1014.3   1014.8   1028   890.1   125.4503089
208   1019.2   1011.2   1032   894.4   117.4992766
209   1024.1   1007.6   1036   898.7   109.5482542
210   1029   1004   1040   903   101.5972441
211   1033.9   1000.4   1044   907.3   93.64624926
212   1038.8   996.8   1048   911.6   85.69527408
213   1043.7   993.2   1052   915.9   77.74432455
214   1048.6   989.6   1056   920.2   69.79340943
215   1053.5   986   1060   924.5   61.84254199
216   1058.4   982.4   1064   928.8   53.89174334
217   1063.3   978.8   1068   933.1   45.94104918
218   1068.2   975.2   1072   937.4   37.99052513
219   1073.1   971.6   1076   941.7   30.04030626
220   1078   968   1080   946   22.09072203
221   1082.9   964.4   1084   950.3   14.14284271
222   1087.8   960.8   1088   954.6   6.203224968
223   1092.7   957.2   1092   958.9   1.838477631
224   1097.6   953.6   1096   963.2   9.732420048
225   1102.5   950   1100   967.5   17.67766953
226   1107.4   946.4   1104   971.8   25.62654873
227   1112.3   942.8   1108   976.1   33.57647986
228   1117.2   939.2   1112   980.4   41.52685878
229   1122.1   935.6   1116   984.7   49.47746962
230   1127   932   1120   989   57.42821606
231   1131.9   928.4   1124   993.3   65.37904863
232   1136.8   924.8   1128   997.6   73.32993932
233   1141.7   921.2   1132   1001.9   81.28087106
234   1146.6   917.6   1136   1006.2   89.23183288
235   1151.5   914   1140   1010.5   97.18281741
236   1156.4   910.4   1144   1014.8   105.1338195
237   1161.3   906.8   1148   1019.1   113.0848354
238   1166.2   903.2   1152   1023.4   121.0358625
239   1171.1   899.6   1156   1027.7   128.9868986
240   1176   896   1160   1032   136.9379421
241   1180.9   892.4   1164   1036.3   144.888992
242   1185.8   888.8   1168   1040.6   152.8400471
243   1190.7   885.2   1172   1044.9   160.7911067
244   1195.6   881.6   1176   1049.2   168.7421702
245   1200.5   878   1180   1053.5   176.693237
246   1205.4   874.4   1184   1057.8   184.6443067
247   1210.3   870.8   1188   1062.1   192.595379
248   1215.2   867.2   1192   1066.4   200.5464535
249   1220.1   863.6   1196   1070.7   208.49753
250   1225   860   1200   1075   216.4486082
251   1229.9   856.4   1204   1079.3   224.3996881
252   1234.8   852.8   1208   1083.6   232.3507693
253   1239.7   849.2   1212   1087.9   240.3018518
254   1244.6   845.6   1216   1092.2   248.2529355
255   1249.5   842   1220   1096.5   256.2040203
256   1254.4   838.4   1224   1100.8   264.155106
257   1259.3   834.8   1228   1105.1   272.1061925
258   1264.2   831.2   1232   1109.4   280.0572799
259   1269.1   827.6   1236   1113.7   288.0083679
260   1274   824   1240   1118   295.9594567
261   1278.9   820.4   1244   1122.3   303.910546
262   1283.8   816.8   1248   1126.6   311.861636
263   1288.7   813.2   1252   1130.9   319.8127265
264   1293.6   809.6   1256   1135.2   327.7638174
265   1298.5   806   1260   1139.5   335.7149088
266   1303.4   802.4   1264   1143.8   343.6660006
267   1308.3   798.8   1268   1148.1   351.6170929
268   1313.2   795.2   1272   1152.4   359.5681855
269   1318.1   791.6   1276   1156.7   367.5192784
270   1323   788   1280   1161   375.4703717
271   1327.9   784.4   1284   1165.3   383.4214652
272   1332.8   780.8   1288   1169.6   391.3725591
273   1337.7   777.2   1292   1173.9   399.3236532
274   1342.6   773.6   1296   1178.2   407.2747476
275   1347.5   770   1300   1182.5   415.2258422
276   1352.4   766.4   1304   1186.8   423.176937
277   1357.3   762.8   1308   1191.1   431.128032
278   1362.2   759.2   1312   1195.4   439.0791273
279   1367.1   755.6   1316   1199.7   447.0302227
280   1372   752   1320   1204   454.9813183
281   1376.9   748.4   1324   1208.3   462.9324141
282   1381.8   744.8   1328   1212.6   470.88351
283   1386.7   741.2   1332   1216.9   478.8346061
284   1391.6   737.6   1336   1221.2   486.7857023
285   1396.5   734   1340   1225.5   494.7367987
286   1401.4   730.4   1344   1229.8   502.6878952
287   1406.3   726.8   1348   1234.1   510.6389919
288   1411.2   723.2   1352   1238.4   518.5900886
289   1416.1   719.6   1356   1242.7   526.5411855
290   1421   716   1360   1247   534.4922825
291   1425.9   712.4   1364   1251.3   542.4433795
292   1430.8   708.8   1368   1255.6   550.3944767
293   1435.7   705.2   1372   1259.9   558.345574
294   1440.6   701.6   1376   1264.2   566.2966714
295   1445.5   698   1380   1268.5   574.2477688
296   1450.4   694.4   1384   1272.8   582.1988664
297   1455.3   690.8   1388   1277.1   590.149964
298   1460.2   687.2   1392   1281.4   598.1010617
299   1465.1   683.6   1396   1285.7   606.0521595
300   1470   680   1400   1290   614.0032573

[Julie]

Aw, come on Dave! That's nothing but numbers. Stop trying to scare people. And why is line 223 in the data twice?

[Andy]

goal seek to find the lowest possible d as a function of the variables in the original worksheet.

it's actually aset of really simple linear formulas, it was just the first large sampling I could find.

[Julie]

what's d? I don't want to read everything above.

[Andy]

distance between two bodies as they move toward (and then away from) each other at different trajectories/rates

[Julie]

What about bessel functions? Would you be better at bessel functions than Tom?

[dave from knoxville]

Aw, come on Dave! That's nothing but numbers. Stop trying to scare people. And why is line 223 in the data twice?

Hey Julie,

This is me over here! I didn't put those numbers up there, Andy did.

Also, I love you.

[Steve of Bloomington]

Bessel functions have something to do with drum heads, right?

Curse you, aging brain!

[Shaggy 2 Grote]

This thread just got awesome!!