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Homework Statement
Well, we are given the following system, in which the rope, spring, and pulley is ideal. We know that for the angle [itex] a [/itex] the system is in equilibrium. The question is, to show that if the angle a is small, the system does unfirom oscilations.
I don't know how to tackle this problem, it confuses me a little. We must show that the resultant force on the body is proportional to a constant and the displacement for the equilibrium position at a given time.
Homework Equations
Some basic trigonometry, with some tricks for aproximating the trigonometric function for small angles and basic vector addition, I think...
The Attempt at a Solution
Well, the first thing that is obvious is that if the system is at rest, then:
[itex] T\cos{a} = ky_0 [/itex] , where y_0 is the initial comprimation of the spring, and k is its spring constant.
Writing the resultant force for the body we get that: [itex] R = T  mg [/itex]. How do I continue from here? Can somebody help me, please :D ?
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