Simple Harmonic Motion - Spring-Pendulum-Mass System

[cpin11]

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.

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

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.

 

[John Park]

Draw a picture if it helps.

Since you're given the force constant for the spring it might be easier to consider the forces on the bob.

 

[gneill]

From the READ ME pinned thread for this forum:

Members are free to work on these older homework threads. Know that none of these problems are relevant to the OP because of their age. So it's best not to ask the OP questions because they likely won't respond, but they may. The point is that you should work with what you are provided to solve the problems without the OP's input. Members are encouraged to collaborate with others within the thread. Creative and alternate methods are also encouraged. Full solutions are acceptable.