100%(7)7 out of 7 people found this document helpful
This preview shows page 4 - 8 out of 11 pages.
6. The position graph should show a sinusoidal, if it has flat regions or spikes, reposition the Motion Detector and try again;7. Fit a sinusoidal curve and record on Table II your values of A, B, and C;9. Using your values of A, B, and C determine the frequency and period of oscillation.Record the period Tand frequency fof this motion in your data table;10. On Table III (for PHY2048L only) write the equations of y(t)and v(t);11. Repeat Steps 1 – 10 with different five other masses.DATA: Length of the Spring: L0= 0.13 mReal Constant: 20.0 N/mTable I: Hooke’s LawTrials123456Mass m(kg)0.200 kg0.400 kg0.600 kg0.800 kg1.00 kg1.20 kgForce on the SpringFs(N)1.96 N3.92 N5.88 N7.84 N9.80 N11.8 NLengthL(m)0.180 m0.280 m0.380 m0.480 m 0.570 m0.665 mIncrease in LengthΔL (m)0.0500 m0.150 m0.250 m0.350 m0.440 m0.535 mTable II: Oscillation
Trials123456Massm(kg)0.200 kg0.400 kg0.600 kg0.800 kg1.00 kg1.20 kgA(m)0.0412 m0.0374 m0.0491 m0.0411 m0.0541 m0.0487 mB(rad/s)9.76 rad/s7.00 rad/s5.74 rad/s5.33 rad/s4.47 rad/s4.11 rad/sC(rad)3.99 rad3.73 rad3.53 rad4.59 rad4.83 rad5.94 radT(s)0.628 s0.889 s1.09 s1.26 s1.40 s1.54 sT2 (s)0.394 s20.790 s21.19 s21.59 s21.96 s22.37 s2f(Hz)1.59 Hz1.13 Hz0.919 Hz 0.800 Hz0.712 Hz0.650 HzEVALUATION OF DATA:Graph 1: Force on the Spring vs. Displacement Equation:Fs(N)=k(Nm)∆ L(m)+b(N)Relationship: The force on the spring is directly proportional to the displacement (linear relationship). Slope:The slope of the line represents the spring constant (k) which is in Newton’s per meter. Y-Intercept: The y-intercept is close to 1 N. There may be some errors when measuring the lengths of the spring for each trial.
Graph 2 (Power): Period vs. MassEquation:y=axkT=A LBRelationship: The graph is a power function and in order to make it linear, I have to squarethe period. As seen on the graph, the function is a side opening parabola where the y axis squared (T2) is proportional to the x axis (M). Therefore, to make this function linear (to make it fit into the equation of the line y=mx+b), the period must be squared to have a proportional relationship. (Note: Proportional means linear.) Once I have the linear graph, I will know the relationship, the equation, and the slope of the line.Graph 2 (Linear): Period Squared vs. Mass