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ds C1<br />
= h<br />
d C1 = 0<br />
d2s 2C2<br />
d 2 = h<br />
2 = 0 C2 = 0<br />
Applying the conditions at = _<br />
or<br />
or<br />
or<br />
s = hC3 <br />
<br />
<br />
3<br />
C3 +C4 +C5 = 1<br />
ds 3C3<br />
= h<br />
d<br />
<br />
<br />
<br />
<br />
<br />
+C4 <br />
<br />
3C3 + 4C4 +5C5 = 0<br />
d2s 6C3<br />
d 2 = h<br />
2<br />
<br />
<br />
<br />
2<br />
+ 4C4<br />
<br />
4<br />
+ C5 <br />
5<br />
<br />
3<br />
<br />
<br />
+12C4<br />
<br />
<br />
6C3 +12C4 + 20C5 = 0<br />
Solving for the constants,<br />
2<br />
C3 =10; C4 = 15; C5 = 6<br />
Therefore,<br />
s = h 10 <br />
<br />
<br />
3<br />
15 <br />
<br />
If h=2 in and = 90˚, then,<br />
( ) 3<br />
s = 210 <br />
<br />
90<br />
4<br />
15 ( 90)<br />
4<br />
<br />
<br />
3C3<br />
<br />
= h<br />
<br />
<br />
2<br />
+6 <br />
<br />
+ 20C5<br />
2<br />
5<br />
( ) 5<br />
+6 <br />
90<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
= hC3 [ +C4 + C5 ]= h<br />
+ 4C4<br />
<br />
<br />
<br />
3<br />
- 353 -<br />
+ 5C5<br />
<br />
6C3<br />
= h<br />
<br />
<br />
<br />
<br />
= 0<br />
2 +12C4<br />
20C5<br />
2 +<br />
2<br />
<br />
<br />
= 0<br />
Here, is assumed to be given in degrees. Note that the values for h and do not enter the<br />
problem until the last step.
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