this post was submitted on 08 May 2025
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Yes, if you think of the depicted spring with dead coils in the centre, as two springs of half length combined, they decrease the stiffness of the combined springs, as two springs in row have only half the stiffness.
My thought was starting from the opposite: A spring with the same number of coils, but equally spaced. At its ends, the axial force onto the spring is converted into internal torque. By Hooke's law, torque and shear strain (here change of twist angle with the coordinate running along the wire) are linked. This twist causes the coiled spring to contract.
However, in the spring with the "dead" coils, this motion is limited to the free coils, as the twist of the "dead" coils is inhibited by their contact. They behave like they were rigid. Thus, there only the wire of the free coils contributes to the (compressive) stiffness of the spring, which is less than the total amount of wire, yielding into a stiffer spring.