Homework Help: Pendulum and spring oscillation

1. Apr 28, 2010

smhippe

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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!

2. Apr 28, 2010

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.