Machine Design
Two closely coiled helical springs with stiffness k₁ and k₂ respectively are connected in series. The stiffness of an equivalent spring is given by

(k₁ - k₂)/ (k₁ + k₂)
(k₁ + k₂)/ (k₁ k₂)
(k₁ k₂)/ (k₁ + k₂)
(k₁ - k₂)/ (k₁ k₂)

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Machine Design
The shear stress at a point in a shaft subjected to a torque is

Directly proportional to the applied torque and the polar moment of inertia
Directly proportional to the polar moment of inertia and to the distance of the point from the axis
Directly proportional to the applied torque and inversely proportional to the polar moment of inertia
Inversely proportional to the applied torque and the polar moment of inertia

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