Is Hooke’s law obeyed, even approximately, by a diving board? A trampoline? A coiled spring made of lead wire?

Yes, the Hooke’s law is obeyed even approximately, by a diving board and a trampoline. But it is not obeyed in the case of coiled spring made of lead wire.
The motion of a body is said to be periodic if it passes through similar conditions after equal intervals of time. Simple harmonic motion is periodic in nature. In accordance to Hooke’s law, with in elastic limits, tension is proportional to extension from the equilibrium position and always points toward the equilibrium position.
In the case of diving board and trampoline when we apply force, the extension produced by this force is proportional the applied tension from the equilibrium position with in elastic limits. That is why; diving board and trampoline obey Hooke’s law. But in the case of coiled spring made of lead wire, the extension produced by tension from equilibrium position is not proportional to the extension with in elastic limits. That is why coiled spring made of lead wire does not obey Hooke’s law.