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Biomechanical engineers developing artificial limbs for prosthetic and robotic applications have developed a two-spring design for their replacement Achilles tendon. The first spring has constant k and the second ak, where a > 1. When the artificial tendon is stretched from x = 0 to x = x1, only the first spring is engaged. For x > x1 a mechanism engages the second spring, giving a configuration like that described in part (a) of Chapter 4’s Problem 62. Find an expression for the energy stored in the artificial tendon when it’s stretched a distance 2x1.
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