Integrate Equation 9.17 in Example 9.2 numerically and make a plot of the speed versus the time using dimensionless parameters, x √2gb vs. t/√2b/g where √2b/g us the free fall time, t free fall. Find the time it takes for the free end to reach the bottom. Define natural units by τ ≡ t√g/2b, a ≡x/2b and integrate dτ/da from a = ε (some small number greater than 0) to a = ½. One can€™t integrate numerically from a = 0 because of a singularity in dτ/da. The expression dτ/da is

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