Question

An experiment was conducted to measure the weight of the water in a cylindrical can. The
water drained out through a small hole in the bottom of the can. Find the quadratic best
fit to the following data obtained from the experiment:

Time (in seconds) Weight of 6 11 16 21 26 31 36 41 47 water in 2.85 2.74 2.63 2.46 2.35 2.24 2.14 2.03 1.97 1.92 Newtons)

Answer 1

The general foim o quadratis best fit is given by ga at batch² ->0 where, a,b and care constants to be determined The Normal equations o are Eyi na + b En; t cami Elig; = achitben ter o and Ezty = acmtb 22 CENY Hove the values of Eyi, Eli, Em, ani, ani, Eni y; and Eniti come calculated below. 3 li yi 2141 ay; 3132 285 1 285 2.85 1296 6 2.74 16.44 36 98-64 216 11 2-63 28.93 12) 1331 14641 318.23 16 2146 39.36 256 4096 65536 629.76 21 2.35 49.35 441 9261 194481 1036:35 26 2.24 58.24 676 175 76 456976 1514.24 31 2:14 66:34 961 29791 923521 2056.54 36 2.03 73.08 1296 46656 1679616 2630.88 41 1.97 80.77 1681 68921 2825761 3311. 57 103823 424).28 47 1.92 90.24 2209 24 = EY; = {x9 = EN = INPE 505-607671 281672 4879681 2014 11041510 Entry; 15840.34 236 123.33

G substitute above values in 0.3 . weget 외 coa + 236 b + 7678C = 23.33 → Czrn=10) 236 9 + 7678 b + 2816720 = 505.60 (6 76789 + 281672 b + 11041510 C = 15840.34 → solving above equations, we get a = 2-9074 b5 -0.0398, C=0.000 2 substitute a,b,c in , we get co 2.9076 +(-0.0308)2 + (0.002)ą? data best fit of given which in the required by least square methode