M9 lab report

M9 Simple Harmonic Motion VI-I Holder mass: m H = 5 g Spring mass: m s = 2.8 g Flag mass: m f = 3.5 g X 0 = 39 cm σ x0 = ±0.1 cm M (g) X m (cm) X = x 0 - x m (cm) 20 36.5 2.5 40 34 5 60 31.5 7.5 80 28.9 10.1 100 26.3 12.1 120 23.5 15.5 0 2 4 6 8 10 12 14 16 18 0 20 40 60 80 100 120 140 f(x) = 7.85 x + 1.08 M vs X M vs X Linear (M vs X) X (cm) M (g) Slope = 7.847233 Slope uncertainty = 0.22922 Y-intercept = 1.075133 Y-intercept uncertainty = 2.246218 Y=sx+b S= (k)(g)

K = s*g K = (7.847233 g/cm)(980 cm/s 2 ) = 7690.29 g/s 2 σ k = (g)(σ s ) σ k = (980 cm/s 2 )(0.22922 g/cm) = 224.64 g/s 2 K = 7690.29 g/s 2 ± 224.64 g/s 2 VI-II m (g) m t (g) C 1 C 2 C 3 N 1 N 2 N 3 T 1 (s) T 2 (s) T 3 (s) T 1 2 (s 2 ) T 2 2 (s 2 ) T 3 2 (s 2 ) 40 48.5 237 240 239 97.2 5 97.2 5 96.2 5 0.61 7 0.61 7 0.62 34 0.38 069 0.38 069 0.38 863 60 68.5 202 201 203 81.7 5 81.7 5 81.2 5 0.73 39 0.73 39 0.73 84 0.53 861 0.53 861 0.54 5234 80 88.5 178 177 178 69.7 5 67.2 5 70.2 5 0.86 02 0.89 22 0.85 41 0.73 994 0.79 602 0.72 9487 100 108. 5 160 160 161 65.7 5 63.7 5 65.7 5 0.91 255 0.94 12 0.91 25 0.83 275 0.88 586 0.83 265 120 128. 5 148 148 148 58.7 5 59.2 5 59.2 5 1.02 128 1.01 27 1.01 26 1.04 301 1.02 556 1.02 5359 N 1 = (2(C 1 – 1)+1)/4 N 1 = (2(237 – 1)+1)/4 = 97.25 T = 60.00/N T 1 = 60.00/97.25 = 0.6170

30 40 50 60 70 80 90 100 110 120 130 0 0.2 0.4 0.6 0.8 1 1.2 f(x) = 0.01 x + 0.06 T^2 vs m T^2 vs m Linear (T^2 vs m) m (g) T2 (s)

Slope = 0.008094 Slope uncertainty = 0.000465 Y-intercept = 0.059488 Y-intercept uncertainty = 0.039416 The figure in the book (which is roughly between 0.333 and 0.405) does not match the amount provided here. This inaccuracy could be caused by a few factors. I can see from my graph that the third and fourth data points are incorrect. They differ a little. This can result in a greater value of and a higher y-intercept. VI-IV d = 2.6 σ d = 0.1 l' l = l' + d/2 C1 C2 C3 N1 N2 N3 T1 (s) T2 (s) T3 (s) T12 (s2) T22 (s2) T32 (s2) 30.5 31.8 104 104 105 36.2 5 36.2 5 37.7 5 1.65 52 1.65 52 1.76 55 2.73 696 2.52 619 1.92 46 39.2 40.5 93 93 93 43.2 5 43.2 5 43.2 5 1.49 068 1.49 068 1.48 068 2.22 213 2.22 213 2.17 23 48.2 49.5 85 86 85 42.2 5 43.7 5 42.2 5 1.42 011 1.54 886 1.42 011 2.01 671 2.11 623 2.01 671 57.1 58.4 78 78 78 38.2 5 38.2 5 38.2 5 1.52 866 1.52 866 1.52 866 2.33 86 2.33 86 2.33 86 69.2 70.5 71 71 71 35.2 5 35.2 5 35.2 5 1.61 073 1.61 073 1.61 073 2.59 445 2.59 445 2.59 445 77.3 78.6 67 67 67 27.2 5 27.2 5 27.2 5 1.83 465 1.83 465 1.83 465 3.36 59 3.36 59 3.36 59