I need help graphing this as well as solving this problem!!! 2. Suppose a studen

Question

I need help graphing this as well as solving this problem!!!

2. Suppose a student recorded the following data during Step 10 of this experiment: A 6.90 deg4.75 deg Time 2.58 deg 8.00 s 1.68 deg 10.0 s 2.00 s 4.00 s 6.00 s The student was careful to start taking data when the angular position of the pendulum was zero. Unfortunately he does not have a computer available to fit the data as you will in Step 12, but she knows that the amplitude of oscillations decays exponentially according to AAe(BC where C-0. Use the data obtained by the student to plot a straight line graph of the appropriate variables on the gratoind vales for the parameters Ap and B. (20pts)

Explanation / Answer

A = A0e-Bt

taking natural logarithm on both sides

=> ln(A) = ln(A0) - Bt

The above equation is of the form y=mx+c where y=ln(A), x=t, m = -B, c=ln(A0)

After plotting time on x-axis and ln(A) on y-axis we obtain,

slope = -0.172

y-intercept = 2.258

Therefore,

-B = -0.172 => B = 0.172

ln(A0) = 2.258 => A0 = 9.56

A 6.90 4.750 3.250 2.580 1.680 ln(A) 1.932 1.558 1.179 0.948 0.519 Time 2 4 6 8 10

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