PHY 151 M9

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M9 Simple Harmonic motion PHY 151 VI-1 # m(g) xm(cm) x(cm)=x0-x m 1 20 37.4 2.4 2 40 34.5 5.3 3 60 31.9 7.9 4 80 29.2 10.6 5 100 26.7 13.1 6 120 24.1 15.7 Sample calculations X= X0-Xm X= 39.8 cm-37.4 cm=2.4 cm Using "LINEST"equation from Excel... Slope(s)=7.5559 g/cm Slope uncertainty, Οƒ s =0.0813 g/cm y-intercept (b)=0.7376 g Οƒ b =0.8311g Spring constant
M9 Simple Harmonic motion PHY 151 mg=kx (from M9-9 Lab Manual) k= or k=sg π‘šπ‘” π‘₯ s= Ξ”π‘š Ξ”π‘₯ 9.8m/s 2 ( )= 980 cm/s 2 100?π‘š 1π‘š Using k=sg k= (7.5559 g/cm)(980 cm/s 2 )=7404.782 g/s 2 k =k √(Οƒ s /s) 2 +√(Οƒ g /g) 2 Οƒ k =(7404.782 g/s 2 )[ √( ) 2 +√( ) 2 ] Οƒ 0.0813 𝑔/?π‘š 7.5559𝑔/?π‘š 0 980 ?π‘š/𝑠2 =(7404.782 g/s 2 )[(1.157 x10 -4 )+(0)]= 0.857 g/s 2 kΒ± k = 7404.782 g/s 2 Β± 0.857 g/s 2 Οƒ VI-2 Comparing both equations below, T 2 = + , y=sx+b 4Ο€2π‘š π‘˜ (4Ο€2)(π‘š)(Ξ±)(π‘šπ‘ ) π‘˜ They are the same equation since s= and b= , 4Ο€2 π‘˜ (4Ο€2)(π‘š)(Ξ±)(π‘šπ‘ ) π‘˜ but in T 2 plot "m" will be the "x" in y plot. # m(g) mt(g) c1 c2 c3 Ci N T T 2 1 40 48.7 221 137 118 158.666 667 79.08 0.7587 0.5756 2 60 68.7 195 197 195 195.666 667 97.58 0.6149 0.3781 3 80 88.7 174 170 162 168.666 667 84.08 0.7136 0.5092 4 100 108.7 155 155 157 155.666 667 77.58 0.7734 0.5981 5 120 128.7 145 145 144 144.666 667 72.08 0.8324 0.6929
M9 Simple Harmonic motion PHY 151 Sample calculations M T = M H +M+M F M T = (5.2g)+(20g)+(3.5)= 28.7g (C 1 + C 2 +C 3 )/3= (221+137+118)/3= 158.66 N= 2(πΆπ‘–βˆ’1)+1 4 N= = 79.08 2(158.66βˆ’1)+1 4 T= = = 0.7587= T 2 = 0.5756 60 𝑁 60 79.08 Using "LINEST"equation from Excel... Slope(s)=0.002273 g/cm Slope uncertainty, Οƒ s =0.001681 g/cm y-intercept (b)=0.3491 Οƒ b =0.1566 Spring constant mg=kx (from M9-9 Lab Manual) k= or k=sg π‘šπ‘” π‘₯ s= Ξ”π‘š Ξ”π‘₯ 9.8m/s 2 ( )= 980 cm/s 2 100?π‘š 1π‘š
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