The position graph should show a sinusoidal if it has flat regions or spikes

The position graph should show a sinusoidal if it has

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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 T and frequency f of 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: L 0 = 0.13 m Real Constant: 20.0 N/m Table I: Hooke’s Law Trials 1 2 3 4 5 6 Mass m(kg) 0.200 kg 0.400 kg 0.600 kg 0.800 kg 1.00 kg 1.20 kg Force on the Spring F s (N) 1.96 N 3.92 N 5.88 N 7.84 N 9.80 N 11.8 N Length L(m) 0.180 m 0.280 m 0.380 m 0.480 m 0.570 m 0.665 m Increase in Length ΔL (m) 0.0500 m 0.150 m 0.250 m 0.350 m 0.440 m 0.535 m Table II: Oscillation
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Trials 1 2 3 4 5 6 Mass m(kg) 0.200 kg 0.400 kg 0.600 kg 0.800 kg 1.00 kg 1.20 kg A(m) 0.0412 m 0.0374 m 0.0491 m 0.0411 m 0.0541 m 0.0487 m B(rad/s) 9.76 rad/s 7.00 rad/s 5.74 rad/s 5.33 rad/s 4.47 rad/s 4.11 rad/s C(rad) 3.99 rad 3.73 rad 3.53 rad 4.59 rad 4.83 rad 5.94 rad T(s) 0.628 s 0.889 s 1.09 s 1.26 s 1.40 s 1.54 s T 2 (s) 0.394 s 2 0.790 s 2 1.19 s 2 1.59 s 2 1.96 s 2 2.37 s 2 f (Hz) 1.59 Hz 1.13 Hz 0.919 Hz 0.800 Hz 0.712 Hz 0.650 Hz EVALUATION OF DATA: Graph 1: Force on the Spring vs. Displacement Equation: F s ( N ) = k ( N m ) ∆ 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.
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Graph 2 (Power): Period vs. Mass Equation: y = ax k T = A L B Relationship: The graph is a power function and in order to make it linear, I have to square the period. As seen on the graph, the function is a side opening parabola where the y axis squared (T 2 ) 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
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