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Physical Lab Report : Harmonic Oscillator Writer: Partner: Experiment date: 26.9.2012&10.10.2012 Report date:13.10.2012Goal of the experiment 1.Get familiar with the air track, Jonlybalance, and timing measurement device. 2.Do some fundamental experiments to check out several relations about Harmonic Oscillator.Principle of the experiment 1.Formula , , , 2. If two springs with spring constants k1 and k2, attaching to both sides of an object.,then the final k=k1+k2Measurements The same steps referred in the passage “Harmonic Oscillator”teacher gave us.Experimental data and analysis 1.Measurement of spring constants Experimental data:K1m/g4.839.6114.419.2324.09X1/cm6.216.216.216.216.21X2/cm8.2210.4812.5214.7216.72K2m/g4.839.6114.419.2324.09X1/cm0.210.210.210.210.21X2/cm2.154.156.068.0310.09K3m/g4.839.6114.4319.2224.0928.92X1/cm3.383.383.383.383.383.38X2/cm5.417.529.6211.6213.715.81Analysis(data processing and graph):K1m/kg0.004830.009610.01440.019230.02409x/m0.02010.04270.06310.08510.1051mg/N0.0473340.0941780.141120.1884540.236082From the graph,we know that k1=2.2202N/m,and R2=0.9995 shows that mg and x are very linearly relative.k2m/kg0.004830.009610.01440.019230.02409x/m0.01940.03940.05850.07820.0988mg/N0.0473340.0941780.141120.1884540.236082From the graph,we know that k2=2.3872N/m,and R2=0.9999 shows that mg and x are quite linearly relative.K3m/kg0.004830.009610.014430.019220.024090.02892x/m0.02030.04140.06240.08250.10330.1244mg/N0.0473340.0941780.1414140.1883560.2360820.283416From the graph,we know that k3=2.2759N/m,and R2=0.9999 shows that mg and x are quite linearly relative.2.Study the relationship between oscillation period and the mass of the oscillatorExperimental datam/g181.1185.89190.68195.51200.2910T/ms12634.112784.412940.513098.513251.2ms/g22.07Analysis(data processing and graph)M=m+ms/3M/kg0.1884566670.1932466670.1980366670.2028666670.2076466671.5962048281.6344088341.6745654031.7157070231.755943014T/s1.263411.278441.294051.309851.32512From the graph,we know that T2 and M are quite linearly relative.And,so =8.3496N/m,we can figure out k=4.7282N/m.And k1+k2=2.2202+2.3872=4.6074N/m,the error rate is 2.62%,which is acceptable .3.Study the relationship between oscillation amplitude and period. Experimental data:m=192.41gms=22.07gA/cm10203035405010T/ms12618.612617.312620.712622.112619.612615.1Analysis(data processing and graph)A/m0.10.20.30.350.40.5T/s1.261861.261731.262071.262211.261961.26151From the graph,R2=0.0303 says that A and T have little relation.4.Study the relation between vmax2 and A2 Experimental datam=192.41gms=22.07gM=m+ms/3=199.77gvmax/cm/s48.896.52143.27166.94190.84239.23A/cm102030354050Analysis(data processing and graph)0.010.040.090.12250.160.250.2381440.931611042.052629292.786896363.641990565.72309929From the graph ,we can know vmax2 and A2 are strictly linearly relative.Discussion and conclusion In this experiment,I have become familiar with some experimental device and have had some results about Harmonic Oscillator: 1.The spring constants are k1=2.2202N/m,k2=2.3872N/m,k3=2.2759N/m. 2. In the range of permitted errors,T2 and M are linearly relative. 3.In the range of permitted errors,A and T have no relation. 4.In the range of permitted errors,vmax2 and A2 are linear
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