Pendulum and spring oscillation

[smhippe]

Homework Statement

A 5 kg sphere is connected to a thin
massless, but rigid rod of length L = 1.3 m to
form a simple pendulum. The rod is connected
to a nearby vertical wall by a spring with spring
constant k = 75 N/m, connected to it at a
distance h = 1.1 m below its point of
suspension. What is the angular frequency (in
rad/s) of the system for small amplitude
oscillations?

Homework Equations

The Attempt at a Solution

So I was listening to my teacher start to solve this problem. He starting talking about summing the torques between these two. I have the equation he wrote down from it, but I am not too sure what to do with it... ($$\tau$$)net = -Lmgsin$$\theta$$ - hk$$\Delta$$xsin$$\beta$$ = m(l^2)$$\alpha$$
Note: alpha is not a power...
I know that the small angle theorum makes sin go away. But how is beta and alpha related? And what about delta x? I don't know I've been working on it for a while and now I'm tired. Thanks for helping!

 

[kuruman]

If you draw the drawing, you will see that you get two right triangles, one above the sphere and one below. They have a common right side that is Δx. Relate this side to L and θ using the top triangle and to h and β using the bottom triangle.