Figure shows a pendulum of length L with a bob of mass M. The bob is attached to a spring of spring constant k as shown. When the bob is directly below the pendulum support, the spring is at its equilibrium length.

(a) Derive an expression for the period of this oscillating system for small amplitude vibrations.

(b) Suppose that M = 1 kg and L is such that in the absence of the spring the period is 2.0 s. What is the spring constant k if the period of the oscillating system is 1.0 s?

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L.