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Figure 3.1 Schematic of a step on a rigid surface (left) and compliant surface (right). Solid line shows the stance leg, broken line shows the swing leg moving forward. Because the foot descends a distance into the compliant track, the step length on the compliant track is necessarily greater. Figure adapted from Figure 5 (McMahon, T. A., & Greene, P. R. (1979). The influence of track compliance on running. Journal of biomechanics, Biomechanics12(12), 893-904893–904.)

(a) Using the figures and description of

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body \delta

 above, derive the expression below for the step length of the runner on a compliant surface,

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body L

, in terms of the runner’s mass,

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body m

, runner’s leg length,

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body l

, the rigid surface step length,

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body L_0

, surface stiffness,

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body k_t

, and local gravitational acceleration,

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body g

.

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(b) Choose some realistic values for

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body m

,

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body l

,

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body L_0

,

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body k_t

, and

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body g

. What is the predicted value for

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body L

? How does this equation predict how

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body L

 will vary with decreasing

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body g

? Discuss how this prediction compares with your intuition.

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title Solution (

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Include Page S3.1 Step length on a compliant surface S3.1 Step length on a compliant surface