I am very much interested in how exactly can one solve harmonic oscillation-problems using solely the KE - PE approach. I am a high-school student, so a little in-depth explanation will very much be appreciated. There seems to be great potential in solving such problems by finding the mass- and elasticity constant equivalent for a harmonic oscillator to find out the period of oscillations and such, but I frankly have no idea nor have I found any clear article on the web for that. So any links to good documentation or tips or some sort of explanations would be very much appreciated!

I have some sample problems that can be solved using this approach, in case they might help any of you make me understand better the process of solving them

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**Sample problem #1:**
The period oscillations of the "swinging" of the surface of a lake around a vertical axis. The dimensions are: L,l (bottom surface), H (equilibrium height), and d (<< H) (the "amplitude" of oscillations). I can sketch a drawing if any of you require.

**Sample problem #2:**
The period of oscillations of a marble (of mass M) that can slide along a string (of length 2L) fixed in two points distance 2d apart. The trajectory is rather obviously an ellipse. The system is set up vertically. (AO = OB = d; AC + BC = 2L - at any given moment)