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**1. Homework Statement**

A pendulum of length L with a bob of mass M hangs vertically. The bob is attached to a horizontal spring that has a force constant k. When the bob is directly below the pendulum support, the spring is unstretched. (a) Derive an expression for the period of the oscillating system for small amplitude vibrations.

**2. Homework Equations**

x = Acos(wt)

w = 2pi/ T

E = 1/2 k A^2

w = sqrt (k/m) for a spring

w = sqrt (g/ L) for a pendulum

**3. The Attempt at a Solution**

I'm pretty sure I need to use energy for this problem but I'm having trouble understanding the system itself.