Question: The figure shows a conical compression helical coil spring where R1 and R2 are the initial and final coil radii, respectively, d is the diameter

The figure shows a conical compression helical coil spring where R1 and R2 are the initial and final coil radii, respectively, d is the diameter of the wire, and Na is the total number of active coils. The wire cross section primarily transmits a torsional moment, which changes with the coil radius. Let the coil radius be given by
R = R1 + R2 ˆ’ R1/2Ï€NaÎ¸

Where Î¸ is in radians. Use Castigliano€™s method to estimate the spring rateas

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